orangeapples said:
emeraldrafael said:
YES! Cause something's missing! What if I lost a toenail? You justs aid that they are different, its just thats tiny. Germs are tiny, do they not exist?
ummm... that's not what I meant. the difference between you and you losing a strand of hair is so small that it pretty much does not exist. you are (1 whole) - (1 strand of hair). The strand of hair is small enough to not make a difference. You are still 1 whole.
in the example you make, the germ is the 1 whole, therefore it (no matter how small) exists.
Alright. Then if i were missing a single cell in my body, would i still be the same? Maybe, maybe not, dependingon the cell and its importance. But the fact that I'm missing it is what makes me not what I was before it was gone.
So, my college professor, who has been teaching at the college for what he says is 40 years, but administration says he's been there 50 years. Either way, he's head of our math department and does a bunch of those lecture things since the guy's easily.. like... 70, if not 80, at other colleges. ANd here's how he explained it to me, which is in my words, not his, so dont get on my back about if I didnt phrase this right and he's dumb. But I will give it to you in the same way he gave to me, which was a numbered list becuase he now thinks I'm retarded since he said he covered this in college algebra and I wasnt listening (even though I clearly remember this).
1: Infinity is range, not a number. Its something to encompass everything, and to say something is never ending, since some smartasses like to add an extra zero to a number and say the made a new number. Infinity has no value, but is rather the combination of all values (which, i guess if you think about it still brings infinity to a value of zero since all numbers would cancel out their positive/negative forms).
2: HUmans, by nature, like things to have value, or physical existence. They dont like the concept of God because he's not tangible. They like numbers in the same way, which is why we dont like to play with imaginary numbers, because I cant say to you that Johny has one imaginary apple. YOu take that as johny pretends to have an apple, which means he has none and is insane to beleive otherwise.
3: Hence, humans can not be happy and satisfied with the number infinity as it is not a value, but range. You can not have infinity dollars physically in the same regard as you can have 1, 2, 5, 10, 100, a million dollars in your hand to hold. Those numbers are tangible, which is what humans like, as it helps them to relate.
4: .999...! =/= 1 in the sense that they have values. 1 > .999....! because it is not the whole one when you look at it on the plain of values in numbers (compared it to have .999...! % of an apple. Though it maybe tiny and insignificant, its still not the whole apple).
5: Numbers have values when pulled from infinity. Infinity in and of its self is another plain of mathematical reality, as it is range that does not top and is hard to tell where it even began, because infinity doesnt have a starting value.
6: Therefore, .999...! = 1 in the plain of range. However, much the same in the plain of infinity as a range, 1 is no different then 10 and is no different then -67. in the range of infinity, where nothing has range or value, -67=1=10 because there is no physical measurement. However, when you look at a number, you are giving it value. 1 is a value, you have one of something. 2 is a value, you have 2 of something (apples, again). if you place two physical apples down on one table, and one physical apple on the other, you have more apples on the first table because you can see and measure it. This is (what he calls) the human value plain of math, where numbers have value, a starting and an ending point.
7: Because you give a number value when you pull it from infinity, it does not equal another unless they are the same value, no matter how close the numbers are. .999...! =/= 1 on the human value plain because if you were to put to separate cups, one with each value, the one with 1 (liter, cup, gallon, pint, whatever) will have more and weigh more then the cup with .999...! since you have given it value.
On the infinity plain of math, you can have both equal, because nothing has value. The human mind doesnt have to look at it as two apples against one. or .999...!th of an apple against 1 whole apple. BUt when you work with numbers, you give them value. Even imaginary numbers have imaginary value, but because they are imaginary it makes it difficult to do anything with them the same way you do "real" numbers.
If you want to look at it another way, its like the difference between the plains of 2D and 3D. You have a line/rod (a 2 dimensional object that when talking about a line is on the infinite plain, while a rod is on the value plain, as it as beginning and ending), can not exist in a 3 dimensional world on a 3 dimensional plain because it misses a dimension. It appears flat to the human mind, and will always appear on a 2D plain. A brick, 2x4, even pencil, anything that is perfectly straight and level that you can physically hold is a 3 dimensional line. In much the same way, 3D can not exist on a 2D plain. You can not have a cube on a single piece of paper that pops out from a single drawing. All "3D" art/paintings are flat objects that appear 3D through optical illusion. However, if you try to grab it, its still flat. Its two separate plains, each with its own rules and meaning of existence/value/definition of what makes something what it is.
So no, .999...! can not equal 1 exactly unless you go up to the infinite plain where numbers lose value. TO ask it then, you have to say does a portion of infinity equal another portion of infinity, without giving a specific value to it. To say it in the way .999...!=1 is to mix two plains of reality that dont mix on simple basis that one has a separate definition of reality then the other.
SO yeah, thats what he said, thats what I'm going with. You're mixing separate plains. its like trying to mix 3D with 2D. Trying to make a 2D object pop out into 3D, and trying to make something 3D out of a flat 2D object.
