Register to reply 
Alternative Proof to show any integer multiplied with 0 is 0 
Share this thread: 
#1
Jan3114, 11:59 PM

P: 255

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: 255




#4
Feb114, 12:26 AM

P: 1,622

Alternative Proof to show any integer multiplied with 0 is 0



Register to reply 
Related Discussions  
Proof for determinant of a scalar multiplied by a vector  Calculus & Beyond Homework  2  
Show that if n is a positive integer, then C(n,0) < C(n,1) <...<C(n, floor(n/2)) = C  Precalculus Mathematics Homework  3  
Show by induction that a given polynomial is an integer  Calculus & Beyond Homework  5  
Proof Question: Prove integer + 1/2 is not an integer  Calculus & Beyond Homework  4  
N=a²+b²c², show that it's true for any integer n,a,b,c  General Math  7 