**
**
*Interesting Mathematics Questions for High School
Students*

Prime Numbers

Question: How many prime numbers are there?

Answer: Infinite!

Question: Can you prove there are infinite prime numbers?

Principle of Mathematical Induction

When we have to prove a mathematics theorem, Mathematical
Induction is one of the useful proofs.

It is done by proving that the first statement in the
infinite sequence of statements is true, and then proving that if any
one statement in the infinite sequence of statements is true, then so is
the next one.

Let *S*(*n*) denote the statement involving the
integer variable *n*. The Principle of Mathematical Induction
states:

If *S*(1) is true and, if for
each integer *k *≥ 1, *
S*(*k*+1) is true whenever *S*(*k*) is true; then
*S*(*n*) is true for all n ≥ 1.

However, the induction itself is also a 'theorem'.

Question: Do you know how to prove the Mathematical Induction?

Lines and Dots under Euclidean geometries

We know that line is made up of dots.

The question
is: How many dots are there in a segment of line?

The answer is:
Infinity.

If it is infinity, then does it mean that all lines are
made up of the "same number" of dots - infinite numbers of dots?
Can you prove it?