Infinity is rational and a real number

1 x 1=1
1 / 1=1
infinity x 1=infinity
infinity / infinity=1

wouldnt this make infinity rational? if they are infinity is divisable by itself, and it makes 1, that means that it has an some sort of whole number which makes it 1.

As my opponent used number systems as his proof, I will discuss only that.

A number system is any compilation of objects that have basic properties (e.g. addition, multiplication) that we normally associate with numbers.

Number systems appear in many sizes. There are "natural number systems", which are the set of numbers used in counting: 1, 2, 3, etc. You can develop this system to consist of additional concepts, like negative numbers, fractions.
Each of these concepts exists, provided we look for it in the framework of a large enough number system.

Does infinity exist in the same manner that these concepts (negative numbers, fractions, etc.) do? Or, "does there exist any number system which, as well as including the familiar numbers we are used to, also includes an "infinity" concept?"

The answer, simply, is no.

What would infinity minus 1 be? It can not be a finite number, as no finite number, plus 1 equals infinity. Therefore:

infinty - 1 = infinty

The rules of arithmetic have to be violated, because if they held, you could subtract infinity from both sides to conclude -1 = 0, which is false.

Consequently, there is no number system which possesses the usual rules of arithmetic and in which infinity exists.

http://www.math.toronto.edu...

Yes, i see your point about infinity - 1 = infinity.
But if infinity wanst real, then there is no such this as infinity, like if it never exist. Which means that there is no such thing as unlimited of anything.
But if it is, then it is a real number and the equation would be infinity - 1= finite.

"Yes, i see your point about infinity - 1 = infinity.
But if infinity wanst real, then there is no such this as infinity, like if it never exist. Which means that there is no such thing as unlimited of anything.
But if it is, then it is a real number and the equation would be infinity - 1= finite."

Ok, I'll make this quick.
Infinity is in this case a concept, it has no value, to have a value one could easily answer what infinity -1 is equal to, additionally, what infinity + 1 is equal to. As the answer must always return infinity (you can not say what number is arrived at) infinity as a number does not exist. Additionally finite is not a number, it is a term you can not use "finite" as a mathematical number. Again, what is finite – 10, still finite, NOT a discrete number. Infinity is not a discrete number, it has no value.

Who ever said that infinity can never exist? Why cant we ever have an infinite amount of stuff? If it cant exist in our universe, it might as well exist in another. So if it did exist in another universe, then that means the universe doesnt exist, since the infinity is not real.

Another favorite question of mine:
Why not?

vote pro

If we refer back to my opponents actual premise:

"Infinity is rational and a real number"

What is not under discussion here is the concept of infinity, or its validity as a term, what my opponent seems to have forgotten is he was trying to show that infinity was a number.

His proof? Infinity/Infinity = 1 and this therefore proves its value as a discrete number.

fgowsnm/fgowsnm = 1 Have I proved the exitence of fgowsnm? Of course not. Just because we can input a term into an equation means nothing at all.

Infinity is the set of all numbers, it has no intrinsic discrete value, it is not a number in and of itself. It has importance in some fields of mathematics sure, but we are not debating those here. My opponent got side tracked, lost and has forgotten to argue his premise.

Regards, Spiral.