h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

zero was created when it was discovered that we needed to rationalize an existing natural phenomenon.

So it was discovered that it needed to be created.

that seems to make sense to me, so I guess to my simple human brain... it was both.

i think zero is more like phylosophical than mathematical. so when humans began to think about eternity they also began to think about zero. and the answer to the question: guess it's discovered.

Sure zero's philosophical. But the fact is that it's a concept that is required to make mathematics work. As is infinity. Take either of these 'philisophical numbers' away, and mathematics simply falls apart.

Which tells us first and foremost that mathematics is a flawed system. It's very useful, but its flawed, and only once you realise that can you use it properly.

I've read a book all about it. According to it, Babylonians first used it, but just as a place holder not an actual number by itself.

Divisions by 0 are normally undefined: there simply isn't an answer. But what you can do is look at the answer of a/b and see what the function does as b approaches 0 from either side.

To say that .9 repeating equals 1 is like saying that if you remove one grain of sand from a beach the weight of the beach has not changed.

The exactness of math and numbers exists only on a theoretical level. You may hold one apple in each hand but the oneness does not make the two identical.

Thus, 1 does not equal 1.

(except when equating apple pi)

"Equal" does not mean "identical to". It means "the same size as".

0.999 recurring is the same size as 1. Subtracting one from the other, you get zero.

I'm with you, Gnomon.

And, to use the previous example:

If you remove one grain of sand from a beach of infinite size the weight of the beach has not changed. [infinity - x = infinity]

In reality there is no infinate beach; a beach around a circular lake will seem infinate if you try to walk to the end. Upon closer inspection one will find that every sand may be counted to apply to a finite total.

.9 repeating subtracted from 1 (or technically, 1.0 {zero repeating}) is not 0. There is a remainder (even if it is one of the smallest fractions).

But, if .9 repeating equals 1; what is .3 repeating (or .6)?

I think 0.3 repeated would be equaling 0.4.

0.333 repeating is equal to one third.

Yep, I realized that after posting. All that stuff about limits in mathematics.

To state one third is certainly logical but what is ten divided by three?

0.9 recurring = 1? Thankfully proper mathematicians have already run up against this one and come up with limits, infinitessimals and set theory. Not all infinites are equal either (which unfortunately means you can't just cancel them ).

But I would support the comment about the apples. In my opinion, 1 apple + 1 apple = 2 apples only so far as the yucky green things in your hands approximate an apple.

Let me adjust my problem to more clearly present my gist;
What is one divided by three. (1/3)

and just for kicks, anyone know why the zeroth root of any number is 1?

The zeroth root of any number is one, because it's the number divided by itself.

So, x^2 (x-squared) is x times x

x^1 can be thought of as x-squared divided by x, which is, of course, x.

x^0 can be thought of as x divided by x, which is 1.

But what if x=0?

RF

Still 1, I think.




But I don't know either.

So, the only power of 0 that does not equal 0 is...er...0?

RF