0^0

I'm not saying abolish it, I'm saying it should be treated differently. If we stopped trying to use it as an integer then we get rid of all the problems. It's a fairly new addition to mathematical symbolic logic. It isn't really a quantity, measure, etc.

$0^0$ is defined to be $0/0$ which is undefined for good reason.

It isn't really a quantity, measure, etc.

well yes it is
a + 0 = a
a * 1 = a

0 works perfectly under addition just like 1 under multiplication.

0^0 and 0/0 and k/0 undifined undefined because 0 doesn't really "work" with multiplication because f: x*0 -> 0 is a many to 1 function thus does not have an inverse. This does not mean that 0 isn't a quantity, and most definately does not mean it is not an integer.

Also this question comes up every few months it gets really annoying.

Your argument is going nowhere.

It is a quantity. I have zero apples on the table. I know because I counted them.

It is a measurement. The distance between two touching objects is zero centimetres.

Bring me nothing of something. I challenge you.

I just did. I delivered it to you without you even noticing.

I'm tiring of this a little but if you want to get technical zero has to be considered as an integer.

The set of integers is closed under addition. This means if you add two integers you always get another integer.

-5 + 5 = 0 hence 0 is an integer. Case closed.

since when?

Also here are the lecture notes to a lecture titled "Is there such a thing as infinity?" which goes into some of the maths involved here

0 can't be represented as the quotient of two other values, so it's not a rational number. I know you can say a/0 = 0 but I don't really agree with that result either, on the same principle that I don't think 0 should be treated as a standard, natural integer.

If you made those notes yourself then **** you because they are useless.

On another note, I noticed you are predicted A*'s - are you supposed to put them on UCAS?

0 can't be represented as the quotient of two other values, so it's not a rational number. I know you can say a/0 = 0 but I don't really agree with that result either, on the same principle that I don't think 0 should be treated as a standard, natural integer.

0 terminates as 0, and is a single digit number. One of the properties of an irrational number is that the decimal expansion is infinite. So it can't be an irrational number then.

If 0 was actually a number then we wouldn't be having this debate. If you can't divide another integer by it without contradictions then clearly something is going wrong.

0/0 remains undefined because it's impossible. 0 is not really a number in the sense that 1, 2 and 3 are numbers. 0 is just an item in symbolic logic to represent zero value.

And zero IS a rational number because it can be expressed as in the form a/b.

Here is an example:

0/5 = 0

Oops another daft theory in the bin.

... 0 is vital for arithmetic without 0 negative numbers don't really have a meaning as the negative (-x) of a number x is defined as x + (-x) = 0.

division isn't a basic function in that division by x is defined as multiplying by the multiplicative inverse where the multiplicative inverse (1/x) is defined as the value such that x*(1/x) = i where i is the multiplicative identity (i.e i = 1). 0 does not have an inverse as but it is still a number, I don't really see why you question 0 being a number any more than you question multiplication.

0 though most definitely being a number is not treated as normal numbers i.e. just as sqrt(-1) is a number but not a normal number. I think the problem might be that you feel numbers are things that really "exist", in truth all numbers are quite abstract concepts they are just used to model situations, just because the behaviour of 0 or sqrt(-1) doesn't match situation that you can relate to does not mean they are conceptually erroneous.

What I'm trying to say is that the concept of 0 doesn't represent a quantitative value and if we didn't try to treat it in the same way we would a concept that maps on to a concrete value then we'd abolish most of the 0 problems.