NUmber theory image

NUmber theory image

Postby matqkks » Thu Dec 12, 2019 7:44 am

Are there any good images that can be used as a hook for an elementary number theory course?
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Re: NUmber theory image

Postby Guest » Thu Dec 12, 2019 11:51 am

Attachments
Real Numbers.png
Real Numbers.png (35.49 KiB) Viewed 422 times
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Re: NUmber theory image

Postby Math Tutor » Fri Dec 13, 2019 1:56 am

That image is incorrect.
Here is a correct one
https://www.math10.com/en/algebra/numbers.html

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Re: NUmber theory image

Postby Guest » Fri Dec 13, 2019 2:57 am

Math Tutor wrote:That image is incorrect.
Here is a correct one
https://www.math10.com/en/algebra/numbers.html


Key Idea: Set size means set abundance for the sake of simplicity (layman's terms) ignoring rigorous math (countable and uncountable sets, dense, etc.)

Natural numbers are less abundant than the integers; integers are less abundant than the rational numbers; rational numbers are less abundant than the algebraic numbers, and finally, algebraic numbers are less abundant than the transcendental numbers. Therefore, we can see the above image as a hierarchy of set abundance or set size from the smallest set, the set of all natural numbers, to the largest set, the set of all transcendental numbers.

Thus, the image above is good!
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Re: NUmber theory image

Postby Math Tutor » Fri Dec 13, 2019 8:42 am

Rational numbers are not a subset of irrational because of that that image is wrong.

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Re: NUmber theory image

Postby Guest » Fri Dec 13, 2019 11:11 am

Math Tutor wrote:Rational numbers are not a subset of irrational because of that that image is wrong.


You do not understand... We are talking about relative set sizes and not subsets... And the image is good!
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