There are vast resource on math for almost every topic there is out there.
I like the clearly formatted information in there, and nicely presented proofs for many interesting theorems there.
Reviewing my elementary math book on the problem of 00 here, I decided to see wiki says:
http://en.wikipedia.org/wiki/Defined_and_undefined#Zero_to_the_zero_power
This is a bit shocking to me:
Modern textbooks often define 00 = 1. For example, Ronald Graham, Donald Knuth and Oren Patashnik argue in their book Concrete mathematics:
"Some textbooks leave the quantity 00 undefined, because the functions 0x and x0 have different limiting values when x decreases to 0. But this is a mistake. We must define x0 = 1 for all x, if the binomial theorem is to be valid when x = 0 , y = 0, and/or x = −y . The theorem is too important to be arbitrarily restricted! By contrast, the function 0x is quite unimportant."
I am no Donald Knuth or the other famous guys. A peak at Donald Knuth's multi-volume classic books on computer science will make most so called "computer science majors" faint. But I beg to differ on their view on 00.
Evaluate 00 on your calculator you will likely get an error.
Here are two conflicting rules about division when x=0:
Rule 1: zero raised to anything is 0. Zero multiply by itself, however many times, is still 0.
Rule 2: anything raised to 0 is 1.
Rule 2 works because you can write x0 as x1 - 1 = x / x = 1.
But watch out, this trick only works when x is non zero.
In the case of 00, there is a conflict here: which rule win? Since rule 2 involves a division by 0, an invalid move. So I think mathematics should not allow 00.
For binomial theorem, why bother define it for x and y = 0, or x+y=0?
Also, if you define exponents xy = exp(y ln x). Plug in x=0, y=0. ln 0 is undefined, so it doesn't work either. So I insist 00 is not defined.
Ok, back to real world, I am sure nobody cares whether 00 is defined or not.
2 comments:
just to let you know that I care. Many middle school teachers teach that anything to the zeroeth power is 1, but anyone who has taken calculus knows that it is indeterminate. Zero has unique properties, and it just might pique a student's interest in math if he realizes that there are exceptions to the rule.
Sorry to disappoint you. I also thought that evaluating 0**0 on most programs and calculators would give you NaN, like e.g. zero division does, but it seems 1 is actually the most common result. :(
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