Unknown number devided by 2 = SOME OTHER unknown number.
It might be accepted that I/2=I, And in the context of infinity being all possible numbers, it is correct. BUT, It is incomplete.
In other words.
I = I/2
2I = I
2I/I = I/I
2 = 1
When USED as a number, it doesn't add up.
In this sense. I devided by 2 is I/2 and can't be reduced further.
Disagree? Give me a proof of it. Show me how my proof (that 2 = 1) is wrong. Based on the rules of infinity, it is correct. Since I/2 is I and I devided by I is 1.
2 times 5 devided by 5 is 2.
So. Saying infinity devided by 2 is infinity is purely academic. And I believe, wrong. It is also why you don't often see it in formulas.
It is a logical problem. Since Infinity is the upward edge, the largest possible number, only since there is no largest number, it is just a concept, it is taken that I devided by 2 is I. But that isn't correct. It is half of I. which is unknown, and there for is I/2, and can't be reduced.
But this is all silly anyway. There are several 'kinds' of infinity. You can define infinity so that I/2=I. However, you can't say Infinity devided by 2 is Infinity is algebra.
Lets talk about space-filling curves now....
http://en.wikipedia.org/wiki/Space-filling_curve
It might be accepted that I/2=I, And in the context of infinity being all possible numbers, it is correct. BUT, It is incomplete.
In other words.
I = I/2
2I = I
2I/I = I/I
2 = 1
When USED as a number, it doesn't add up.
In this sense. I devided by 2 is I/2 and can't be reduced further.
Disagree? Give me a proof of it. Show me how my proof (that 2 = 1) is wrong. Based on the rules of infinity, it is correct. Since I/2 is I and I devided by I is 1.
2 times 5 devided by 5 is 2.
So. Saying infinity devided by 2 is infinity is purely academic. And I believe, wrong. It is also why you don't often see it in formulas.
It is a logical problem. Since Infinity is the upward edge, the largest possible number, only since there is no largest number, it is just a concept, it is taken that I devided by 2 is I. But that isn't correct. It is half of I. which is unknown, and there for is I/2, and can't be reduced.
But this is all silly anyway. There are several 'kinds' of infinity. You can define infinity so that I/2=I. However, you can't say Infinity devided by 2 is Infinity is algebra.
Lets talk about space-filling curves now....
http://en.wikipedia.org/wiki/Space-filling_curve