A geometry theory without irrational numbers?Do mathematicians, in the end, always agree?Real Numbers to...
How to show the equivalence between the regularized regression and their constraint formulas using KKT
Where does SFDX store details about scratch orgs?
What do you call someone who asks many questions?
Why doesn't H₄O²⁺ exist?
Today is the Center
How to draw the figure with four pentagons?
Would Slavery Reparations be considered Bills of Attainder and hence Illegal?
Is "remove commented out code" correct English?
How much of data wrangling is a data scientist's job?
Theorems that impeded progress
What exploit are these user agents trying to use?
Will google still index a page if I use a $_SESSION variable?
What to put in ESTA if staying in US for a few days before going on to Canada
A reference to a well-known characterization of scattered compact spaces
Should I tell management that I intend to leave due to bad software development practices?
Anagram holiday
Brothers & sisters
What about the virus in 12 Monkeys?
Could gravitational lensing be used to protect a spaceship from a laser?
Western buddy movie with a supernatural twist where a woman turns into an eagle at the end
Combinations of multiple lists
What mechanic is there to disable a threat instead of killing it?
What killed these X2 caps?
How could indestructible materials be used in power generation?
A geometry theory without irrational numbers?
Do mathematicians, in the end, always agree?Real Numbers to Irrational PowersInfinite irrational number sequences?Do irrational numbers have equivalence classes the way rational numbers do?Are there numbers that if proven rational (or irrational) will have important consequences to mathematics?Are irrational numbers irrational by nature?Rational mean of irrational numbers?Is there a “positive” definition for irrational numbers?Geometric proofs outside euclidean geometryHow many Irrational numbers?Continued fractions of rational vs irrational numbers
$begingroup$
Is there any theory or theorem of geometry -- whether used in practice or not -- which denies or forbids the use of irrational numbers?
If not, were there any notable attempts at it?
Disclaimer: I am not looking for a proof for the existence of irrational number.
geometry math-history irrational-numbers
asked 14 hours ago
Eyal RothEyal Roth
1113
New contributor
Eyal Roth is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
|
show 8 more comments
$begingroup$
Is there any theory or theorem of geometry -- whether used in practice or not -- which denies or forbids the use of irrational numbers?
If not, were there any notable attempts at it?
Disclaimer: I am not looking for a proof for the existence of irrational number.
geometry math-history irrational-numbers
asked 14 hours ago
Eyal RothEyal Roth
1113
New contributor
Eyal Roth is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
2
$begingroup$
A geometrically interesting subset of the real numbers are the constructible numbers, you can find some information on that on Wikipedia and read into it from there if interested. However, these also include some irrational numbers (but not all).
$endgroup$
– Dirk
14 hours ago
2
$begingroup$
Have you heard of finite geometry, as in: en.wikipedia.org/wiki/Finite_geometry ? This is geometry where there are only a fintie numbre of points, hence you can assign them all natural numbers.
$endgroup$
– quarague
14 hours ago
$begingroup$
@quarague Why not add it as an answer? :)
$endgroup$
– Eyal Roth
13 hours ago
$begingroup$
Irrational numbers were discovered during the early development of geometry (finding lengths of hypotenuses of right triangles). This gives an idea how limiting such a restriction would be.
$endgroup$
– Hans Engler
13 hours ago
1
$begingroup$
@EyalRoth That is surely a matter of opinion :)
$endgroup$
– Hans Engler
13 hours ago
|
show 8 more comments
$begingroup$
Is there any theory or theorem of geometry -- whether used in practice or not -- which denies or forbids the use of irrational numbers?
If not, were there any notable attempts at it?
Disclaimer: I am not looking for a proof for the existence of irrational number.
geometry math-history irrational-numbers
asked 14 hours ago
Eyal RothEyal Roth
1113
New contributor
Eyal Roth is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Is there any theory or theorem of geometry -- whether used in practice or not -- which denies or forbids the use of irrational numbers?
If not, were there any notable attempts at it?
Disclaimer: I am not looking for a proof for the existence of irrational number.
geometry math-history irrational-numbers
geometry math-history irrational-numbers
asked 14 hours ago
Eyal RothEyal Roth
1113
New contributor
Eyal Roth is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 14 hours ago
Eyal RothEyal Roth
1113
New contributor
Eyal Roth is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 13 hours ago
Eyal Roth
asked 14 hours ago
Eyal RothEyal Roth
1113
New contributor
Eyal Roth is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 14 hours ago
Eyal RothEyal Roth
1113
asked 14 hours ago
Eyal RothEyal Roth
1113
1113
New contributor
Eyal Roth is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Eyal Roth is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Eyal Roth is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
$begingroup$
A geometrically interesting subset of the real numbers are the constructible numbers, you can find some information on that on Wikipedia and read into it from there if interested. However, these also include some irrational numbers (but not all).
$endgroup$
– Dirk
14 hours ago
2
$begingroup$
Have you heard of finite geometry, as in: en.wikipedia.org/wiki/Finite_geometry ? This is geometry where there are only a fintie numbre of points, hence you can assign them all natural numbers.
$endgroup$
– quarague
14 hours ago
$begingroup$
@quarague Why not add it as an answer? :)
$endgroup$
– Eyal Roth
13 hours ago
$begingroup$
Irrational numbers were discovered during the early development of geometry (finding lengths of hypotenuses of right triangles). This gives an idea how limiting such a restriction would be.
$endgroup$
– Hans Engler
13 hours ago
1
$begingroup$
@EyalRoth That is surely a matter of opinion :)
$endgroup$
– Hans Engler
13 hours ago
|
show 8 more comments
2
$begingroup$
A geometrically interesting subset of the real numbers are the constructible numbers, you can find some information on that on Wikipedia and read into it from there if interested. However, these also include some irrational numbers (but not all).
$endgroup$
– Dirk
14 hours ago
2
$begingroup$
Have you heard of finite geometry, as in: en.wikipedia.org/wiki/Finite_geometry ? This is geometry where there are only a fintie numbre of points, hence you can assign them all natural numbers.
$endgroup$
– quarague
14 hours ago
$begingroup$
@quarague Why not add it as an answer? :)
$endgroup$
– Eyal Roth
13 hours ago
$begingroup$
Irrational numbers were discovered during the early development of geometry (finding lengths of hypotenuses of right triangles). This gives an idea how limiting such a restriction would be.
$endgroup$
– Hans Engler
13 hours ago
1
$begingroup$
@EyalRoth That is surely a matter of opinion :)
$endgroup$
– Hans Engler
13 hours ago
2
2
$begingroup$
A geometrically interesting subset of the real numbers are the constructible numbers, you can find some information on that on Wikipedia and read into it from there if interested. However, these also include some irrational numbers (but not all).
$endgroup$
– Dirk
14 hours ago
$begingroup$
A geometrically interesting subset of the real numbers are the constructible numbers, you can find some information on that on Wikipedia and read into it from there if interested. However, these also include some irrational numbers (but not all).
$endgroup$
– Dirk
14 hours ago
2
2
$begingroup$
Have you heard of finite geometry, as in: en.wikipedia.org/wiki/Finite_geometry ? This is geometry where there are only a fintie numbre of points, hence you can assign them all natural numbers.
$endgroup$
– quarague
14 hours ago
$begingroup$
Have you heard of finite geometry, as in: en.wikipedia.org/wiki/Finite_geometry ? This is geometry where there are only a fintie numbre of points, hence you can assign them all natural numbers.
$endgroup$
– quarague
14 hours ago
$begingroup$
@quarague Why not add it as an answer? :)
$endgroup$
– Eyal Roth
13 hours ago
$begingroup$
@quarague Why not add it as an answer? :)
$endgroup$
– Eyal Roth
13 hours ago
$begingroup$
Irrational numbers were discovered during the early development of geometry (finding lengths of hypotenuses of right triangles). This gives an idea how limiting such a restriction would be.
$endgroup$
– Hans Engler
13 hours ago
$begingroup$
Irrational numbers were discovered during the early development of geometry (finding lengths of hypotenuses of right triangles). This gives an idea how limiting such a restriction would be.
$endgroup$
– Hans Engler
13 hours ago
1
1
$begingroup$
@EyalRoth That is surely a matter of opinion :)
$endgroup$
– Hans Engler
13 hours ago
$begingroup$
@EyalRoth That is surely a matter of opinion :)
$endgroup$
– Hans Engler
13 hours ago
|
show 8 more comments
2 Answers
2
active
oldest
votes
$begingroup$
I don't know how helpful you will find it, but there are videos on YouTube by njwildberger on rational trigonometry. The main idea is to avoid taking square roots and deal with squares of lengths and ratios between them. He calls it quadrance.
https://www.youtube.com/watch?v=GGj399xIssQ&list=PL3C58498718451C47
http://www.wildegg.com/intro-rational-trig.html
Trouble is, the irrational approach seems to be working fine so there is no reason to completely overhaul the system.
answered 14 hours ago
Chris MoorheadChris Moorhead
1095
$endgroup$
8
$begingroup$
It should also be mentioned, however, the njwildberger is considered a bit of a contrarian on the fringes and that one should be ready with a grain of salt when consuming his material. If you (eyal roth, the original poster) do not have a lot of mathematical maturity, his message might be more confusing/distracting than informative. I'm far from an expert on his subject area though, and maybe some of it stands up better than the negative parts I have heard about.
$endgroup$
– rschwieb
13 hours ago
$begingroup$
@rschwieb Thanks for the warning. I'm quite agnostic in nature, so I tend to employ a lot of critical thinking and try to figure out things on my own before I accept a proposition.
$endgroup$
– Eyal Roth
13 hours ago
$begingroup$
@EyalRoth That's good, but even so, keep an eye on your watch as you budget time to sink into that material.
$endgroup$
– rschwieb
13 hours ago
$begingroup$
I agree, he is somewhat eccentric, but I can see the rationale behind some of his objections. I think the rational trig idea is more that he thinks it would be easier to teach because it is more intuitive and teaches you a geometry closer to the Greek's understanding. But for someone who has learned the existing system, it is like trying to learn to write with your other hand.
$endgroup$
– Chris Moorhead
12 hours ago
add a comment |
$begingroup$
Have you heard of finite geometry, as in: en.wikipedia.org/wiki/Finite_geometry ? This is geometry where there are only a finite number of points. So you don't even need rationals, natural numbers suffice.
answered 13 hours ago
quaraguequarague
621312
$endgroup$
$begingroup$
Well, the natural numbers "sort of" suffice. The things that are being used as coordinates in finite geometries aren't really like natural numbers either (there's no order, for example.) . But in terms of there only being finitely many things in the field, yeah, you wouldn't need "as many" things in your system of numbers.
$endgroup$
– rschwieb
13 hours ago
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Eyal Roth is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3174657%2fa-geometry-theory-without-irrational-numbers%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I don't know how helpful you will find it, but there are videos on YouTube by njwildberger on rational trigonometry. The main idea is to avoid taking square roots and deal with squares of lengths and ratios between them. He calls it quadrance.
https://www.youtube.com/watch?v=GGj399xIssQ&list=PL3C58498718451C47
http://www.wildegg.com/intro-rational-trig.html
Trouble is, the irrational approach seems to be working fine so there is no reason to completely overhaul the system.
answered 14 hours ago
Chris MoorheadChris Moorhead
1095
$endgroup$
8
$begingroup$
It should also be mentioned, however, the njwildberger is considered a bit of a contrarian on the fringes and that one should be ready with a grain of salt when consuming his material. If you (eyal roth, the original poster) do not have a lot of mathematical maturity, his message might be more confusing/distracting than informative. I'm far from an expert on his subject area though, and maybe some of it stands up better than the negative parts I have heard about.
$endgroup$
– rschwieb
13 hours ago
$begingroup$
@rschwieb Thanks for the warning. I'm quite agnostic in nature, so I tend to employ a lot of critical thinking and try to figure out things on my own before I accept a proposition.
$endgroup$
– Eyal Roth
13 hours ago
$begingroup$
@EyalRoth That's good, but even so, keep an eye on your watch as you budget time to sink into that material.
$endgroup$
– rschwieb
13 hours ago
$begingroup$
I agree, he is somewhat eccentric, but I can see the rationale behind some of his objections. I think the rational trig idea is more that he thinks it would be easier to teach because it is more intuitive and teaches you a geometry closer to the Greek's understanding. But for someone who has learned the existing system, it is like trying to learn to write with your other hand.
$endgroup$
– Chris Moorhead
12 hours ago
add a comment |
$begingroup$
I don't know how helpful you will find it, but there are videos on YouTube by njwildberger on rational trigonometry. The main idea is to avoid taking square roots and deal with squares of lengths and ratios between them. He calls it quadrance.
https://www.youtube.com/watch?v=GGj399xIssQ&list=PL3C58498718451C47
http://www.wildegg.com/intro-rational-trig.html
Trouble is, the irrational approach seems to be working fine so there is no reason to completely overhaul the system.
answered 14 hours ago
Chris MoorheadChris Moorhead
1095
$endgroup$
8
$begingroup$
It should also be mentioned, however, the njwildberger is considered a bit of a contrarian on the fringes and that one should be ready with a grain of salt when consuming his material. If you (eyal roth, the original poster) do not have a lot of mathematical maturity, his message might be more confusing/distracting than informative. I'm far from an expert on his subject area though, and maybe some of it stands up better than the negative parts I have heard about.
$endgroup$
– rschwieb
13 hours ago
$begingroup$
@rschwieb Thanks for the warning. I'm quite agnostic in nature, so I tend to employ a lot of critical thinking and try to figure out things on my own before I accept a proposition.
$endgroup$
– Eyal Roth
13 hours ago
$begingroup$
@EyalRoth That's good, but even so, keep an eye on your watch as you budget time to sink into that material.
$endgroup$
– rschwieb
13 hours ago
$begingroup$
I agree, he is somewhat eccentric, but I can see the rationale behind some of his objections. I think the rational trig idea is more that he thinks it would be easier to teach because it is more intuitive and teaches you a geometry closer to the Greek's understanding. But for someone who has learned the existing system, it is like trying to learn to write with your other hand.
$endgroup$
– Chris Moorhead
12 hours ago
add a comment |
$begingroup$
I don't know how helpful you will find it, but there are videos on YouTube by njwildberger on rational trigonometry. The main idea is to avoid taking square roots and deal with squares of lengths and ratios between them. He calls it quadrance.
https://www.youtube.com/watch?v=GGj399xIssQ&list=PL3C58498718451C47
http://www.wildegg.com/intro-rational-trig.html
Trouble is, the irrational approach seems to be working fine so there is no reason to completely overhaul the system.
answered 14 hours ago
Chris MoorheadChris Moorhead
1095
$endgroup$
I don't know how helpful you will find it, but there are videos on YouTube by njwildberger on rational trigonometry. The main idea is to avoid taking square roots and deal with squares of lengths and ratios between them. He calls it quadrance.
https://www.youtube.com/watch?v=GGj399xIssQ&list=PL3C58498718451C47
http://www.wildegg.com/intro-rational-trig.html
Trouble is, the irrational approach seems to be working fine so there is no reason to completely overhaul the system.
answered 14 hours ago
Chris MoorheadChris Moorhead
1095
answered 14 hours ago
Chris MoorheadChris Moorhead
1095
answered 14 hours ago
Chris MoorheadChris Moorhead
1095
answered 14 hours ago
Chris MoorheadChris Moorhead
1095
1095
8
$begingroup$
It should also be mentioned, however, the njwildberger is considered a bit of a contrarian on the fringes and that one should be ready with a grain of salt when consuming his material. If you (eyal roth, the original poster) do not have a lot of mathematical maturity, his message might be more confusing/distracting than informative. I'm far from an expert on his subject area though, and maybe some of it stands up better than the negative parts I have heard about.
$endgroup$
– rschwieb
13 hours ago
$begingroup$
@rschwieb Thanks for the warning. I'm quite agnostic in nature, so I tend to employ a lot of critical thinking and try to figure out things on my own before I accept a proposition.
$endgroup$
– Eyal Roth
13 hours ago
$begingroup$
@EyalRoth That's good, but even so, keep an eye on your watch as you budget time to sink into that material.
$endgroup$
– rschwieb
13 hours ago
$begingroup$
I agree, he is somewhat eccentric, but I can see the rationale behind some of his objections. I think the rational trig idea is more that he thinks it would be easier to teach because it is more intuitive and teaches you a geometry closer to the Greek's understanding. But for someone who has learned the existing system, it is like trying to learn to write with your other hand.
$endgroup$
– Chris Moorhead
12 hours ago
add a comment |
8
$begingroup$
It should also be mentioned, however, the njwildberger is considered a bit of a contrarian on the fringes and that one should be ready with a grain of salt when consuming his material. If you (eyal roth, the original poster) do not have a lot of mathematical maturity, his message might be more confusing/distracting than informative. I'm far from an expert on his subject area though, and maybe some of it stands up better than the negative parts I have heard about.
$endgroup$
– rschwieb
13 hours ago
$begingroup$
@rschwieb Thanks for the warning. I'm quite agnostic in nature, so I tend to employ a lot of critical thinking and try to figure out things on my own before I accept a proposition.
$endgroup$
– Eyal Roth
13 hours ago
$begingroup$
@EyalRoth That's good, but even so, keep an eye on your watch as you budget time to sink into that material.
$endgroup$
– rschwieb
13 hours ago
$begingroup$
I agree, he is somewhat eccentric, but I can see the rationale behind some of his objections. I think the rational trig idea is more that he thinks it would be easier to teach because it is more intuitive and teaches you a geometry closer to the Greek's understanding. But for someone who has learned the existing system, it is like trying to learn to write with your other hand.
$endgroup$
– Chris Moorhead
12 hours ago
8
8
$begingroup$
It should also be mentioned, however, the njwildberger is considered a bit of a contrarian on the fringes and that one should be ready with a grain of salt when consuming his material. If you (eyal roth, the original poster) do not have a lot of mathematical maturity, his message might be more confusing/distracting than informative. I'm far from an expert on his subject area though, and maybe some of it stands up better than the negative parts I have heard about.
$endgroup$
– rschwieb
13 hours ago
$begingroup$
It should also be mentioned, however, the njwildberger is considered a bit of a contrarian on the fringes and that one should be ready with a grain of salt when consuming his material. If you (eyal roth, the original poster) do not have a lot of mathematical maturity, his message might be more confusing/distracting than informative. I'm far from an expert on his subject area though, and maybe some of it stands up better than the negative parts I have heard about.
$endgroup$
– rschwieb
13 hours ago
$begingroup$
@rschwieb Thanks for the warning. I'm quite agnostic in nature, so I tend to employ a lot of critical thinking and try to figure out things on my own before I accept a proposition.
$endgroup$
– Eyal Roth
13 hours ago
$begingroup$
@rschwieb Thanks for the warning. I'm quite agnostic in nature, so I tend to employ a lot of critical thinking and try to figure out things on my own before I accept a proposition.
$endgroup$
– Eyal Roth
13 hours ago
$begingroup$
@EyalRoth That's good, but even so, keep an eye on your watch as you budget time to sink into that material.
$endgroup$
– rschwieb
13 hours ago
$begingroup$
@EyalRoth That's good, but even so, keep an eye on your watch as you budget time to sink into that material.
$endgroup$
– rschwieb
13 hours ago
$begingroup$
I agree, he is somewhat eccentric, but I can see the rationale behind some of his objections. I think the rational trig idea is more that he thinks it would be easier to teach because it is more intuitive and teaches you a geometry closer to the Greek's understanding. But for someone who has learned the existing system, it is like trying to learn to write with your other hand.
$endgroup$
– Chris Moorhead
12 hours ago
$begingroup$
I agree, he is somewhat eccentric, but I can see the rationale behind some of his objections. I think the rational trig idea is more that he thinks it would be easier to teach because it is more intuitive and teaches you a geometry closer to the Greek's understanding. But for someone who has learned the existing system, it is like trying to learn to write with your other hand.
$endgroup$
– Chris Moorhead
12 hours ago
add a comment |
$begingroup$
Have you heard of finite geometry, as in: en.wikipedia.org/wiki/Finite_geometry ? This is geometry where there are only a finite number of points. So you don't even need rationals, natural numbers suffice.
answered 13 hours ago
quaraguequarague
621312
$endgroup$
$begingroup$
Well, the natural numbers "sort of" suffice. The things that are being used as coordinates in finite geometries aren't really like natural numbers either (there's no order, for example.) . But in terms of there only being finitely many things in the field, yeah, you wouldn't need "as many" things in your system of numbers.
$endgroup$
– rschwieb
13 hours ago
add a comment |
$begingroup$
Have you heard of finite geometry, as in: en.wikipedia.org/wiki/Finite_geometry ? This is geometry where there are only a finite number of points. So you don't even need rationals, natural numbers suffice.
answered 13 hours ago
quaraguequarague
621312
$endgroup$
$begingroup$
Well, the natural numbers "sort of" suffice. The things that are being used as coordinates in finite geometries aren't really like natural numbers either (there's no order, for example.) . But in terms of there only being finitely many things in the field, yeah, you wouldn't need "as many" things in your system of numbers.
$endgroup$
– rschwieb
13 hours ago
add a comment |
$begingroup$
Have you heard of finite geometry, as in: en.wikipedia.org/wiki/Finite_geometry ? This is geometry where there are only a finite number of points. So you don't even need rationals, natural numbers suffice.
answered 13 hours ago
quaraguequarague
621312
$endgroup$
Have you heard of finite geometry, as in: en.wikipedia.org/wiki/Finite_geometry ? This is geometry where there are only a finite number of points. So you don't even need rationals, natural numbers suffice.
answered 13 hours ago
quaraguequarague
621312
edited 13 hours ago
answered 13 hours ago
quaraguequarague
621312
answered 13 hours ago
quaraguequarague
621312
answered 13 hours ago
quaraguequarague
621312
621312
$begingroup$
Well, the natural numbers "sort of" suffice. The things that are being used as coordinates in finite geometries aren't really like natural numbers either (there's no order, for example.) . But in terms of there only being finitely many things in the field, yeah, you wouldn't need "as many" things in your system of numbers.
$endgroup$
– rschwieb
13 hours ago
add a comment |
$begingroup$
Well, the natural numbers "sort of" suffice. The things that are being used as coordinates in finite geometries aren't really like natural numbers either (there's no order, for example.) . But in terms of there only being finitely many things in the field, yeah, you wouldn't need "as many" things in your system of numbers.
$endgroup$
– rschwieb
13 hours ago
$begingroup$
Well, the natural numbers "sort of" suffice. The things that are being used as coordinates in finite geometries aren't really like natural numbers either (there's no order, for example.) . But in terms of there only being finitely many things in the field, yeah, you wouldn't need "as many" things in your system of numbers.
$endgroup$
– rschwieb
13 hours ago
$begingroup$
Well, the natural numbers "sort of" suffice. The things that are being used as coordinates in finite geometries aren't really like natural numbers either (there's no order, for example.) . But in terms of there only being finitely many things in the field, yeah, you wouldn't need "as many" things in your system of numbers.
$endgroup$
– rschwieb
13 hours ago
add a comment |
Eyal Roth is a new contributor. Be nice, and check out our Code of Conduct.
Eyal Roth is a new contributor. Be nice, and check out our Code of Conduct.
Eyal Roth is a new contributor. Be nice, and check out our Code of Conduct.
Eyal Roth is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3174657%2fa-geometry-theory-without-irrational-numbers%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
2
$begingroup$
A geometrically interesting subset of the real numbers are the constructible numbers, you can find some information on that on Wikipedia and read into it from there if interested. However, these also include some irrational numbers (but not all).
$endgroup$
– Dirk
14 hours ago
2
$begingroup$
Have you heard of finite geometry, as in: en.wikipedia.org/wiki/Finite_geometry ? This is geometry where there are only a fintie numbre of points, hence you can assign them all natural numbers.
$endgroup$
– quarague
14 hours ago
$begingroup$
@quarague Why not add it as an answer? :)
$endgroup$
– Eyal Roth
13 hours ago
$begingroup$
Irrational numbers were discovered during the early development of geometry (finding lengths of hypotenuses of right triangles). This gives an idea how limiting such a restriction would be.
$endgroup$
– Hans Engler
13 hours ago
1
$begingroup$
@EyalRoth That is surely a matter of opinion :)
$endgroup$
– Hans Engler
13 hours ago