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kripkrip420
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Homework Statement
I am using Spivak's Calculus and just finished the third exercise in part 1.
It was a very easy exercise but it seems that Spivak makes some assumptions.
The problem is as stated:
If x[itex]^{2}[/itex]=y[itex]^{2}[/itex], then either x=y or x=-y. Prove it.
The proof was relatively simple (by factoring out (x-y)(x+y) from x[itex]^{2}[/itex]
-y[itex]^{2}[/itex] and showing that either (x+y)=0 or (x-y)=0 or both). What I had problems with was that it was assumed that a(0)=0. So, I will now propose a proof that a(0)=0 for all real a using the properties listed in the book. All I need is a confirmation that my proof haw no flaw. Thank you.
Homework Equations
The Attempt at a Solution
Introduce (a*0).
(a*0)+(a*0)=0+(a*0).
By the distributive law
a(0+0)=(a*0)+0
By the existence of the additive identity
a*0=(a*0)+0.
Subtracting (a*0) from both sides yields
(a*0)-(a*0)=0
And by the existence of additive identity
0=0
Which is true. Is this valid?
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