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/sci/ - Science & Math

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1981180 No.1981180 [Reply] [Original]

I have a question about starting an algebraic mathematical proof:

If I have a quantity that I know to be 0, say a = 0, since a*b = 0 and a*c = 0, regardless of values for b and c, is it acceptable to begin a proof by stating that ac = ab and working algebraically from there? It feels wrong, but I can't really think of any example in which this wouldn't provide an accurate proof.

Pic related, I'm trying to prove something about the Fibonacci sequence

>> No.1981273

I guess you could, but all you're really saying is that 0 = 0, why would you need to explicitly state that?

>> No.1981277

> 0 = 0
> 0*1 = 0*2
> 1 = 2
> trollface.jpg

>> No.1981286

>>1981180
Yes, ac = ab is correct, as 0=0, however, you are not alllowed to divide this expression by a

\thread

>> No.1981292

>>1981277
0/10

>> No.1981293

Yes, it's correct. I'm not sure why you'd need to do this though. Be careful not to divide by zero.

>> No.1981354

awesome, I'm starting with a more complicated expression, namely:

a^(n-2) * (a^2 - a - 1) = (1-a)^(n-2) * (a^2 - a - 1), where a as stated is a root to that quadratic in there. it's part of a proof by induction, and don't worry, no divide by zero in sight