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Any assistance with this following problem would be greatly appreciated. I'm in Year 11 and working through Apostol volume 1.

1. The problem statement, all variables and given/known data

sin n*pi = 0, where n is an integer

sin n*pi =/= 0, where n isnotan integer.

Prove these statements...

2. Relevant equations

Hmm...

3. The attempt at a solution

My idea is that perhaps I need to use set theoretic ideas or mathematical induction, initially to show that the first case holds for all n.

sin 0*pi = 0

sin 1*pi = 0

sin (1+1)pi = 0 = sin (n+1)*pi

sin n*pi = 0

So, sin (n+1)*pi = 0 (where n is an integer)

Now, to use set theoretic notation:

Let sin n*pi = A.

A = {n is an element of R|sin n*pi = 0, n is an integer}

B = {n is an element of R|sin n*pi =/= 0, n is not an integer}

.: A = {0}

.: B =/= {0}

Now, this is circular - I haven't proved anything at all. (sorry for not using latex, unsure about how to write set notation).

Any assistance would be grand.

Cheers,

Davin

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Proving a trig identity: set theoretic ideas?

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