What is the difference in maths between a demonstration and a proof?

Answer 1

Given our hypothesis: An even number multiplied by an even number will always result in another even number.

We candemonstratethat this is true by selecting any two even numbers and multiplying them together:

8 x 10 = 80

Clearly, our demonstration shows that our hypothesis is correct for those two numbers; however, there are aninfinitenumber of integers that must bedemonstratedin order to prove it. Thus, it it necessary to

prove that our hypothesis is true for all numbers.

We can prove our hypothesis by using algebra.

An even number is an integer that is evenly divisible by 2, i.e., divisible by 2 without remainder.

Let n and m be even or odd integers not equal to 0.

Then 2n makes even or odd n even, because it is divisible by 2, without remainder. In the same fashion, 2m is also even. Multiplied together we have

2n x 2m = 4nm.

Therefore, an even number multiplied by an even number will always result in an even number. And we have proved it.