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December 4th, 2011, 07:23 PM   #1
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Properties of Integer Arithmetic

Wondering if you guys can help me out with something very simple. I tried googling this but can't find proper definitions for these, and since I didn't go to grade school here, I've gotten way beyond calculus but never learned English terms for basic arithmetic stuff (terms, which is not to be confused with knowing how to use arithmetic properties ) . Anyhow, the numbers below are arbitrary, and I just need to know what arithmetic property of integers the operations correspond to (by definition):

5+0=5--> additive identity
+5+(-5)=0--> additive inverse
3*0=0--> zero product proerty/multiplication property
5*1=5--> multiplicative identity

These below are the ones I am having trouble with:

a) 5-3=5+(-3) --> substraction???

b) 5*5=(-5)*(-5)-->multiplication with signed integers

c) If 5*3=15 then ( -5)*3= -15 --> same as above, operation(multiplication) with signed integers???

Thanks ahead of time! I realize how trivial this is!
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December 4th, 2011, 09:57 PM   #2
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Re: Properties of Integer Arithmetic

Quote:
Originally Posted by toughcookie723
a) 5-3=5+(-3) --> substraction???

b) 5*5=(-5)*(-5)-->multiplication with signed integers

c) If 5*3=15 then ( -5)*3= -15 --> same as above, operation(multiplication) with signed integers?
There really aren't standard names for these properties.

Note that "substraction" should never be used in any context; the word is "subtraction". I've seen several non-English speakers use it and I'm not sure why. It hasn't been correct English for hundreds of years and isn't understood.

Other than that, your names are fine.
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December 4th, 2011, 10:15 PM   #3
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Re: Properties of Integer Arithmetic

For instance in French you say soustraction and you pronounce the "s". So I guess it is easy to do the mistake to still pronounce the "s" in English even though it is not there, since subtraction and soustraction are very closed world...
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