Originally Posted by SUroot
Thanks for posting that. I know that infinity is used in maths. I think you're missing my point. I did not say your maths was wrong. I said maths in general is wrong. I am completely comfortable arguing this with a college mathematics professor. In fact, thats all the more poignant.
1 is 1. .9999' is not 1. I am using ' as the symbol for recurring as there isn't one.
We cannot use infinity to prove something that is not 1 is actually 1. Infinity is not a number. It is s concept. Recurring numbers do not actually exist. If I have 9 cakes, I can share them between 3 people equally. If I have 2 people, cutting the cake is possible. If I have 10 cakes and 3 people, cutting the cake wont work. It is physically not possible.
Recurring numbers exist so from a mathematical stand point, it is possible when in reality we know the contrary to be true.
So now we have a series of equations that attempt to prove .9999' is equal to 1. The mathematics behind it stands up. My point is, that is irrelevant. Using a non-existant number in an equation to prove that something that really exists is in fact something else, wont wash.
Mathematics is hugely flawed and even the greatest mathematical minds of our time still do not understand it fully. We know 1 is 1. We know .9999' is not 1. We cannot use mathematical flaws (the use of things that cannot exist) to prove otherwise. If all it is doing is "proving" that the opposite of reality is true (incorrectly) then it's use of proving anything lessens significantly. Its credibility is lost.
So you see, its not me against you. Its reality against maths. .9999' is the closest you can get in maths to 1 without being 1 and no amount of mathematical loop holes will change that.
Maths exists in reality and has its uses in everyday life. I do not deny. How else will I share cakes fairly or count in binary?! However as infinity is a concept and not a reality, regardless as to whether we can use it to show something that doesn't exist is the same as something that does exist, doesn't make it conclusive or even correct. You can only use existing numbers in reality to prove conclusively, which I've already shown proves the opposite and that my good man, is my point.
Part of your problem is that you think there are non-existent numbers.
1/3 is not a non-existent number. It is impossible to represent finitely as a decimal number. That's a simple way of saying that it is impossible to represent as a finite sum of powers of 10. If, however, you were to think in terms of base-3, 1/3 is neatly represented as .1
To say that something is not a number simply because it can't be finitely represented in the base system of your choice would be to end computer math as we know it, because there are a *lot* of numbers that can't be finitely represented as powers of 2. 1/5 (.2) is one such number. The nice and neat .2 in decimal is represented by the infinitely repeating (and in your world, "nonexistant") .0011001100110011...
(note, I am well aware that computers don't represent floating point numbers this way).
Man, it's really going to blow some of your minds when you learn that e^i*pi = -1, where i is the square root of -1.