A person of my acquaintance has shown the unfortunate habit of demonstrating ignorance, both in the sense of not knowing something and in the one of (apparently) intentionally ignoring it.
In particular, the willful ignorance of the definitions of both infinity and nothingness. He believes, as many of you do, that those two things are numbers and are also inverses of one another.

I tell you - and you will be able to understand (I hope) - that neither of those two defining statements is true.

Zero is not a number. It is a concept.

Infinity is not a number. It is a concept.

Numbers are used for counting things, and for putting them in order. Any other use may be convenient, but it does not have to do with the idea of “number” as such.

We grow up in the society of today, as we have for a couple to three or four hundred years, with the idea that “fractions” are numbers. We learn in our schools to talk about and think about - and even calculate about - such things as “half” of something, or “three quarters” of something else, and - worse, by far - “fifteen percent” or “0.15″ of yet another thing. Those of us whose education leads into more intensive arithmetic may learn to deal with other ideas that are clearly conceptual even though we learn to treat them as numbers - concepts such as “pi”.

None of these things is a number.

A “fraction”, as we are taught to call it, such as “one half” - or 1/2 as it is written when we look to its use in calculations - is not a number. It is in fact, and quite obviously at that, two numbers and a symbol, namely the numbers “1″ and “2″, and the symbol “/”. If we care to treat it as a single entity, we can call it a “ratio” - although in our modern usage, should we actually run into the idea of the ratio, we usually see the “/” symbol replaced with the “:” symbol, as in 1:2 - and it is specifically the ratio of one to two. If we’re dealing with calculation - which is the near-universal use of the thing, the idea of “half” rears its ugly head, and in the modern era of calculators and spreadsheet programs, it quickly transforms itself into the far worse “0.5″, which rather than being called “one half”, is far more generally called “point five” (less often, “zero point five”, and still less often, “five tenths”).

Even worse, this whole idea of “fractionation”, once it has taken root as some sort of arithmetical operation, degenerates into the assertion that any “fraction” in which the second number is twice as large as the first one is “numerically” equivalent to “1/2″… for example “3/6″. This is, on its very face, completely absurd - no one can possibly believe that an apple divided into two pieces, each identified as “half an apple” and are ridiculously asserted to be identical, which they assuredly are not, are furthermore identically the same as any three pieces of another apple which has been divided into six “equal” pieces… let alone any 50 pieces of an apple divided into a hundred… and so on.

So, to return to that point: one (or 1) is a number; two (or 2) is a number. 1/2 is not a number - it is two numbers and a symbol denoting either comparison or fractionation (dividing).

And while multiple divisions of something may be “equivalent” - that is, the same in some ways - they are not and cannot be “identical” - at least, not insofar as we deal with reality. One half of an apple divided into two pieces is - in reality - obviously and clearly not identical to three sixths of another apple, even if the two apples are indistinguishably identical.

The very “operation” of division of something into parts - which is indicated by the two numbers and the symbol - leads directly to a very important conclusion regarding nothingness and infinity.

First of all, you cannot divide “nothing”, so it is obvious that the first number cannot be “zero” - another way of looking at this is to consider (as do the alleged mathematicians who write the text used in almost all “courses” of maths) that zero (”0″) divided by any number is mathematically identical to zero divided by any other number, and that value is zero; that is to say, regardless of how many pieces you attempt to fractionate zero into, you still have nothing… if you start with nothing, you end with nothing. This should be more or less intuitively obvious, since, if the primary use, or property, of a “number” is to count things or to put them in order, and since you can’t count or order “nothing”, why, nothing (zero, 0) cannot possibly be a number.

More later - I have errands to do.