Sunday, February 26, 2006

Could I Pass 8th Grade Math?

Yes, it turns out. As would Kieran Healy and PZ Myers. But I passed in my standard half-assed fashion getting 9/10 correct. I would, however, cry foul. The quiz claims I got #2 wrong: Is "-7" an integer, whole number, prime number or irrational? I said it was a whole number, but it is also obviously an integer. Given that whole number is a rather vague concept with many definitions that is used only in 8th grade algebra (Wikipedia says it is either all integers, non-negative integers, or positive integers), I'm going to claim victory (in actuality you talk only of integers and their subsets, not whole numbers, but I thought that maybe since whole numbers and integers were both possibilities they had non-standard definitions in this context).

At Crooked Timber there is a weak debate about whether or not "-7" is a prime number. People are getting all caught up trying to divide things by "1" and itself, but the relevant fact about primes is that they provide a unique factorization of any positive integer. If you had both positive and negative primes, then you would not have such a unique factorization (though prime means something slightly different in ring theory, 'cause the important idea is dividing, and not factoring).


Blogger henry said...

A minor point...a number is prime if, when it divides a*b, it also divides a or b. So -7 is definitely a prime number.

12:32 AM  
Blogger Isaac said...

Yeah. That's how we defined it in algebra (what I was trying to get across in the parenthetical remark).

BUT, and here's the problem with the question, in 8th grade algebra it gets defined differently. Because you don't say that a prime factorization is unique up to units, you just say that it is unique (then again, you are never asked to factor negative integers).

12:37 AM  

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