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What is meant by the word proof?

By Lisa Kelly on the 11th of June, 2012

2 Answers

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    If you prove something then you show without doubt that it's true. This is a stronger statement than a demonstration.

    Example
    I have a bag with exactly 5 blue counters in it.

    If I take out one of the counters and show you it's blue then I have given a demonstration that there are 5 blue counters in the bag (but I haven't proved it!)

    If I take out all 5 and show they are blue and then show you that the bag is empty, then I have proved that there are 5 blue counters in the bag only.

    Refine By Lee Mansfield on the 14th of June, 2012

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    A proof is a series of mathematical statement showing the a theorem definition is in fact true.

    Refine By Lini on the 19th of January, 2013

Suggested reading…

Understand the difference between a demonstration and a proof

Using algebra, it is possible to prove that some things will always be true, this is sometimes referred to as algebraic proof questions. 

For example, let’s start with the hypothesis that an even number multiplied by an even number will always result in another even number.

We can demonstrate that this is true by selecting any two even numbers and multiplying them together:

4 x 10 = 40

40 is even, therefore our hypothesis holds. But, no matter how many examples we choose, we will never prove that it is true, because there may yet be two even numbers we could select which in fact don’t result in an even number.

We can only prove our hypothesis by using algebra.

2n is a multiple of 2, therefore must always be an even number. 2m is also a multiple of 2, therefore must always be another even number.

2n x 2m = 2nm

nm is just another unknown number, it could be odd or even.

2nm is a multiple of 2, therefore must always be an even number.

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

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