We show that the set of all mappings from a set to itself with composition as an operation is a monoid, but not a group.

# Tag: proof

## Nilpotent Implies Singular

We show, step-by-step, how to prove that if a matrix is nilpotent, then it must be singular. We then provid the write up of this proof.

## Induction Proof

We show, step-by-step, how to use induction to prove that an equation holds for all natural numbers.

## Integers written as 13x+10y

We show, step-by-step, how to determine if all integers can be written in the form 13x+10y. We then show how to prove our answer.

## Disproving a Theorem

We show, step-by-step, how to determine if a function has the property that it will always be prime. We then prove the answer we find.