We show that the set of all mapping of real numbers with the operations of sums and products forms a commutative ring with identity.

# Category: Proofs

We look at simple yet elegant proofs that show the creativity and beauty of mathematics.

## Are those really the same size?

We compare the size of the sets of natural numbers, integers, rational numbers and real numbers.

## A number bigger than infinity!

We show that there is something bigger than infinity.

## What are the integer solutions of x^{4}+y^{4}=z^{4}?

We show that Fermat's Last Theorem holds for the case n=4.

## Fundamental Theorem of Arithmetic

We show that every natural number can be factored uniquely into the product of primes.