The divide-by-zero paradox

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You were going to say I said the Indians invented nothing

I thought that these days they tended to construct numbers and arithmetic from set theory.

So:
Let 0 = { } = the empty set
Let 1 = { 1 } = { the empty set }
Let 2 = { 2 } = { { the empty set } }
Let n+1 = { n }

I can't remember how negative numbers are constructed.
I think fractions are constructed as pairs (you can build pairs out of sets). Etc. Etc.

I don't believe that any one invented math. It was an extension of our development of counting.

I has 1 rocks. I has 2 rocks. I throw. I has 1 rock.

It was probably in terms of one, few, or many at first. There was few mammoth? No, there was maaaaany! ARGH!

The concept of quantity is the origin of math, in my opinion. And since this came from a practical need then it was also economics. These days we just have more complex forms of counting.

Yesterday I counted to 12, or "a dozen" as they say in Europe. With more research I hope to be up to 27 by the end of this year. Wish me luck.

Another issue I was curious about is when did people began to use the concept of infinity? Like words like "forever" in the Bible we assume people meant infinity but was "forever" really just a very long time in most peoples minds eye and not in fact an infinite amount of time? Only a person that is a mathematical historian and fluent in Greek and /or Hebrew maybe able to answer

I don't know what this things about who invented maths. It is has nothing to do with that. It is well documented that zero wasn't an automatic concept in early civilisations. We are talking about zero as we use it now. It may seem obvious but it wasn't until a positional system of numbers came in did they even begin to develop zero.

Actually the some Australian aboriginals have a very short number system 1, 2 anything else is many or much.

I'm not sure I think of infinity as a way of representing forever but it get complicated when people talk of types of infinity. Relative infinity, etc.

Use ordered pairs and equivalence relations.
Similar to the fractions.
eg. (a,b) ~ (c,d) iff a+d=b+c.

Yes, it's rather a large subject.
The concept of infinity wasn't properly defined until recent years ( 1800s ).
It's amazing that the greeks missed it. I think it was archimedes (it's a long time since i read this) who devised a system of dealing with absolutely massive numbers ( much bigger than atoms in the known universe).
But they never actually took the small step left to define infinity. However, they were quite secretive with some knowledge and never liked to write things down ( all word of mouth). So, it's possible that they were aware of the concept.
Nowadays, definitions of infinity are taught without really grasping how large these large numbers can get.

I just read something where someone was talking about her four year old daughter asking about infinity. The 'experts' said because she was four she wouldn't understand and also wouldn't understand negative numbers. One of the 'experts' said say infinity is a very big number. If your four year old child asks about infinity why not try to explain?

Yes it was my fault for bringing it up. Nothing to do with the issue of zero.
Just a philosophical question best left to philosophers.
Some mathematicians think about such things, but only on the weekends.

This page contains some of the different perspectives (mathematical realism)...
http://en.wikipedia.org/wiki/Mathematical_realism

It's actually a common indicator of mathematical ability.
Four is very young to talk of such things as infinity.
But questioning whether there are more even numbers than odd numbers and similar such things is an indicator. I remember walking down the street and noting all the evens on one side, odd on the other.
Predicting the next house number and so forth.
The 'expert' probably had less grasp of infinity than the four year old.

What? Syntax Error.

There is no paradox.

The real number field under the standard operations only really has two operations; addition and multiplication.

Division is just multiplication by the multiplicative inverse; 0 doesn't have a multiplicative inverse in R so the question of dividing by zero is meaningless (in conventional real arithmetic).

If you are referring to L'Hopital's Rule then this isn't strictly true; L'Hopital's Rule deals with limits.

w0t r U n00Bz t4Lk1nG ab0Üt z3r0 i$ @ L3773R 0n t3h internets.

Rules can be applied in order. The one that you have is fine. Deal with it.