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462chevelle

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- Thread starter 462chevelle
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- #1

462chevelle

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- #2

lurflurf

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- #3

462chevelle

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the way I would prove that.

because an even number times an even number equals an even number.

sounds terrible I know..

- #4

Mark44

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Why?the square of an even number is even.

the way I would prove that.

because an even number times an even number equals an even number.

Any even number n can be written in the form n = 2k, for some integer k. (An odd number can be written in the form 2m + 1.)sounds terrible I know..

What do you get when you square 2k? Can you convince yourself that the result is also even?

There are a couple of books that might be helpful to you: The Nuts and Bolts of Proofs, and How to Read and Write Proofs. You should be able to do a web search on those titles and come up with the authors and other info.

- #5

eddybob123

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I read them both

- #6

verty

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- #7

1MileCrash

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the way I would prove that.

because an even number times an even number equals an even number.

sounds terrible I know..

That's not a proof at all, it's an assertion.

If you set out to prove that the square of an even number is an even number, you start from what an even number is, and what a square is, and show that it is even.

You can't assume that an even number times an even number is an even number, because you are assuming what you are trying to prove in the guise of a slightly more general statement.

- #8

462chevelle

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you're right. that is where my language barrier suffers.

- #9

HallsofIvy

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If I were asked to prove that "the product of two even numbers is an even number", the first thing I would think about is the

So- do

(Saying that "2, 4, 6 are even numbers" or "even numbers are numbers like 2, 4, 6" are NOT definitions.)

- #10

462chevelle

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would you care to define an even number for me?

- #11

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It is a number which can be factored as ##2n##, where ##n## is an integer.would you care to define an even number for me?

- #12

Edgardo

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Here's a thread with lots of links to material on proofs:

How to write math proofs

How to write math proofs

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