# NUmber theory image

### NUmber theory image

Are there any good images that can be used as a hook for an elementary number theory course?
matqkks

Posts: 1
Joined: Thu Dec 12, 2019 7:41 am
Reputation: 0

### Re: NUmber theory image

Attachments
Real Numbers.png (35.49 KiB) Viewed 422 times
Guest

### Re: NUmber theory image

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

Math Tutor

Posts: 413
Joined: Sun Oct 09, 2005 11:37 am
Reputation: 28

### Re: NUmber theory image

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!
Guest

### Re: NUmber theory image

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

Math Tutor

Posts: 413
Joined: Sun Oct 09, 2005 11:37 am
Reputation: 28

### Re: NUmber theory image

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!
Guest