
Re: 0^0 in the schoolroom
Posted:
Nov 5, 2013 10:27 PM


On Wednesday, October 23, 2013 1:56:15 PM UTC7, konyberg wrote: > On Wednesday, October 23, 2013 9:05:50 PM UTC+2, quasi wrote: > > > Shmuel wrote: > > > > > > >Peter Percival wrote: > > > > > > >> > > > > > > >>How do schools deal with it now? The answer might be > > > > > > >>different in different parts of the globe... > > > > > > > > > > > > > >The answer might be different in different schools withing the > > > > > > >same country, especially for federal countries like the USA. > > > > > > > > > > > > I doubt that you can find a standard USA text for a course such > > > > > > as, say, Intermediate Algebra or Precalculus which asserts > > > > > > > > > > > > a^0 = 1 for all a > > > > > > > > > > > > Rather they say it this way: > > > > > > > > > > > > a^0 = 1, a != 0. > > > > > > > > > > > > An important organization that helps set standards for math > > > > > > at the Precollege level is the NCTM (National Council of > > > > > > Teachers of Mathematics). > > > > > > > > > > > > Another key organization is the College Board which creates > > > > > > standard national tests such as the SAT. > > > > > > > > > > > > The above organizations command wide respect, which partly > > > > > > explains the lack of variation among standard texts with > > > > > > respect to the basic laws of algebra. > > > > > > > > > > > > For subjects such as Biology, certain states in the US mandate > > > > > > that precollege schools use textbooks which present both > > > > > > "Darwinian Evolution" and "Intelligent Design" as competing > > > > > > theories, discussed on an equal footing. > > > > > > > > > > > > But high school math in the US has largely avoided such > > > > > > politically motivated meddling. > > > > > > > > > > > > quasi > > > > Yes, keeping the rules consistent is one reason to define 0^0 =1. But isn't the binomial theorem based on this fact, and since it is a theorem one can use it to show that 0^0=1? Or at least defined as 1. > > > > I know that D. E. Knuth meant that 0^n was of no interest, but n^0 was of great interest. > > > > KON
Please excuse 0^0, .999, and lim 1/x x x>oo = 1 if they are poorly explained. They aren't, that's why everybody uses the same definitions. Zero to the zero, point nine nine nine, limit infinity 1/x * x = x/x = 1, here I mention these and casually people find contradictions with mathematics and
x^0 = 1 0^x = 0
with
0^0 = ( 0 or 1 )
here to say it's only one and not the other instead of the one or the other. Then, in writing the symbol, put the vector bold on either the exponent or base or prime here the base of the logarithm. So of course as a student, I obviously explained what it was.
Then people point out that one or the other is not so, with of course of something that's mathematically so. Sure, zero to any power is zero, this is what it equals zero. In the approximations here on the primes, and, how they are roots to zero, then they equal one. That's how it seems, as matter of fact. It's whether the sum or the product goes to zero (here the exponent, combinatoric). Whether the effect of the relevant term of that the scalar is the parameter, as to the order of magnitude, it is either as relevant. There are distributions, parameters, and constants, generally in effect there are componentizing terms. These are just numbers they are naturally that with simple diagrams like the circle pi is its constant.
Of course, it makes sense to go on as the proof is a mathematical result where it maintains what it holds as true. In powers all the numbers, to the zero, go to one. The number to the one or first power is the number, the number to the zeroeth power = 1. But, at zero it is discontinuous, where the function for zero of the field of the exponent, which is flat and zero, to equal anything else then at 0^0, that is 0 to the 0. Basically I'm trying to figure out if I'm worse in adequacy or competency.
Regards, Ross Finlayson

