Highschool math .. or .. The Power of Nothing
June 18th, 2007 | 
Author: 
We all know from our highschool math classes that:
1. x0 = 1 for any value of x (not very intuitive, but easy to prove)
and
2. 0x = 0 for any value of x
Considering rule 1 and 2: what, then, is the value of
00?
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Posted in Math, Numbers, Random remarks, Riddles
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“it depends” is the right answer 🙂
http://mathforum.org/dr.math/faq/faq.0.to.0.power.html
but 1 is good enough, it seems, for most of the time
@Injun .. I never got good grades in school by answering questions that way 😉
It is also the answer that is ALWAYS followed by the question: “on what?”
to which the next answer would be: “the way you look at it” (Or, as in this case: “who you ask”)
@Injun .. “it depends” appears to indicate that in order to answer the question of which rule to apply (since they clearly can’t be applied BOTH, as that would lead to the absurdity of saying 1 = 0), one has to make certain assumptions.
Interestingly … my $5 pocket calculator REFUSES to make ANY assumptions and simply flags the operation as an – ERROR -.
@myself .. Of course, one can hardly expect a calculator to become philosophically creative .. for only five bucks!
Where am I going with all this?
First of all: we have to admit .. the problem was stated wrongly.
“for any value of x” SHOULD have been: “for any value of x, other than 0”.
But that doesn’t invalidate the question: what is 00!
This all has some deep philosophical implications:
We start with NOTHING, and “do” something to it, involving only one other quantity, which happens to ALSO be nothing.
As my wife pointed out .. the result can ONLY be … NOTHING: whatever the operation: if you “do” NOTHING to NOTHING… NOTHING happens (I have to believe she was referring to her ignored requests for me to empty the dishwasher).
But then Injun’s references seem to indicate that it is mathematically okay to assume that the answer is 1.
And there ARE indeed some very good reasons for that as well…
So, can we get something out of nothing? And suddenly .. there we have my subscript to my post about ‘free energy’ (which simply claims, in Latin, “no”).
Yet .. here we are!
WHERE did we come from? Nothing?
And then the interesting idea from the most accurate and precise (so far) ‘law of nature’ (Quantum Physics) tells us there is no such thing as ‘nothing’ (along with other incrompehensible facts, but nevertheless astonishingly correct in its predictions).
So, maybe the Greek were right in not even considering ‘0’ and the Indian people (sorry Yuvi 😉 were wrong about introducing it…
And if you think ZERO is controversial… don’t even get me started on negative numbers!
(All this was inspired by my Credit Card company’s statement!)
.. Oh, and in case one or some of my very good religious friends consider(s) to answer the question “where do we come from” with a referral to God’s creation .. I then do demand to be explained where God came from. And the answer that he, as necessary for to create anything, has always been there, is a self-defeating proposition, or, when taken to its logical conclusion admits that something can exist without being created, which in and by itself negates the need for a creator.