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October 24th, 2009, 05:30 PM   #1
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mathematical proofs

So, I dont know if this is the correct place to put this, if not, mods could you please put it in the right sub forums.

I'm in a mathematical proof class, and we've been starting on proofs, of the two column variety.
I missed a couple of classes due to the flu, and am now way behind. I plan on going into the professor, but I was wondering about some very basic proofs like -(-a) = a. what would be the correct list of steps for something like that?

Also, here are a couple others.
(-a)b = -(ab)
Using the the theorem -(a) = (-1)a, I can write (-a)b as (-1)(a)(b). Then using associativity, i can rewrite that as (-1)(ab) and that is equivalent to -(ab). It seems too simple, am I missing steps, or just going about this all wrong?

a + a + 2a. Would this one just be using the definition of 1? Saying that 1 x a = a. then a + a must equal 2a?

How would you write a proof of (a^-1)^-1 = a if a is nonzero?
How about If a < b, then -a > -b?

Thank you so much
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October 24th, 2009, 11:46 PM   #2
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Re: mathematical proofs

Quote:
Originally Posted by wontonsoup
So, I dont know if this is the correct place to put this, if not, mods could you please put it in the right sub forums.
It might be better in the abstract algebra section... but it doesn't quite seem to fit anywhere.

Quote:
I'm in a mathematical proof class, and we've been starting on proofs, of the two column variety.
I missed a couple of classes due to the flu, and am now way behind. I plan on going into the professor, but I was wondering about some very basic proofs like -(-a) = a. what would be the correct list of steps for something like that?
Basically, do the same thing you did for (-a)b=-(ab)

Quote:
Also, here are a couple others.
(-a)b = -(ab)
Using the the theorem -(a) = (-1)a, I can write (-a)b as (-1)(a)(b). Then using associativity, i can rewrite that as (-1)(ab) and that is equivalent to -(ab). It seems too simple, am I missing steps, or just going about this all wrong?
No. It really is that simple. These things may seem tedious and obvious now, but before too long you'll be seeing structures which aren't so familiar and you can't take all of these properties for granted. So these proofs are actually pretty good prep for that... it makes you think about what's really happening behind the scenes.

Quote:
a + a + 2a. Would this one just be using the definition of 1? Saying that 1 x a = a. then a + a must equal 2a?
Use the definition of one, and then "pull out" the a.

Quote:
How would you write a proof of (a^-1)^-1 = a if a is nonzero?
How about If a < b, then -a > -b?
For the first one, you are trying to show that a is the inverse of a^-1. What does the relationship between a number and it's inverse look like?

For the second one, you really do exactly what it looks like you need to do. (Think about 8th grade )


Quote:
Thank you so much
Not a problem.

Cheers
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