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Alternative Proof to show any integer multiplied with 0 is 0 
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#1
Jan3114, 11:59 PM

P: 253

In his book, Spivak did the proof by using the distributive property of integer. I am wondering if this, I think, simpler proof will also work. I want to show that ##a \cdot 0 = 0## for all ##a## using only the very basic property (no negative multiplication yet).
For all ##a \in \mathbb{Z}##, ##a+0=a##. We just multiply ##a## again to get ##a^2+(a \cdot 0) = a^2##. Then it follows ##a \cdot 0 = 0##. (I remove ##a^2## by adding the additive inverse of it on both side) 


#2
Feb114, 12:04 AM

P: 1,622

That is essentially the same proof as the one given in Spivak. I have no idea what simplification you think it affords.



#3
Feb114, 12:13 AM

P: 253




#4
Feb114, 12:26 AM

P: 1,622

Alternative Proof to show any integer multiplied with 0 is 0



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