qafir said:
First off, I already explained in detail how numbers (functions, actually) "approach" zero, or infinity, or any other defined or undefined point.
numbers or functions? because the way that 0.(9) is created has nothing to do with a function, son. it's a progression. which is something entirely different. a progression can represent a number if it converges to a limit (which then will be the represented number). a function is something entirely different. in some cases, you can convert a progression into a function but this would in fact move it even further away from the number-thing.
you better take your calculus book again and check the words you want to use.
qafir said:
I actually wanted to double-check myself yesterday, and I pulled out an English Calculus text. It uses the term "approaches."
i'm sure the word "approaches" will appear somewhere in this book. but i'm just as sure that it isn't applied to the word "number". if so, i would like to see a scan.
qafir said:
Any time you graph a function, you use "motion" words to describe following the function along the graph.
okay and where in this whole problem do you see a function?
qafir said:
Second, 0.999! never equals 1.
i know. the difference is 0.0001. and what's the difference between 0.(9) and 1? because we aren't talking about 0.999. at least i'm not. and vaxer surely wasn't, either.
qafir said:
Second, 0.999! never equals 1. They do not have the same definition. But for all intents and purpose, they are TREATED as the same thing. The test of this is simple. Please refer to my above suggestion that you insert the defined value of c (0.9999999...) back into the equation to verify that the solution is correct. If you do so, you find that while in the original proof, 10c-c=9c=9, that conclusion is not verified if you multiply (9 x 0.99999999...). You always get 8.999... UNTIL you arbitrarily choose a decimal place and round to that point. THEN you get the answer 9.
this is a logical fallacy. if you put "c" in and get "c" out, it doesn't mean that "c" isn't the very same thing as one. 8.(9) is the same thing as 9.
if you "round" this means making one number a different one. a "different" number must have a "difference" to the original number. so what is the difference?
qafir said:
I agree, in the original proof presented, 10c-c = 9. This is a mathematical simplification. Please see my above comparison to treating pi as a three digit number for calculations when we all know it's a randomly repeating infinite decimal.
what you refuse to understand is that when you round pi, you will get:
"rounded pi"-pi=x and x>0, no matter at what decimal you round pi.
when you say:
0.(9)-1=x then x=0.
qafir said:
I We do not use these simplifications (rounded-off numbers) because they ARE equal. We use them because there is no other way of handling complex equations.
i don't know who "we" are, but *i*, personally, as a maths student, never use rounded numbers. the reason for this is simple: i don't calculate with real numbers anymore. most of the time everything is written in variables. you can "round" in physics. not in maths. and if i write 0.(9)=1 this doesn't mean i'm too lazy to make a difference. it is absolutely one and the same thing. that 0.(9) LOOKS different to 1 mostly is a flaw of decimal notation.
qafir said:
So come on...You know as well as I do that you don't object to my math. You hate me personally.
sure. your maths is correct. everybody who disagrees must be a hater. earth IS flat.
i've given you three simple questions. they were:
Jay R. Zay said:
- what fraction other than 1 equals 0.(9)?
- what's the difference "1 - 0.(9)"?
- how can a number move, approach, ...?
you didn't answer any single one of them. why? because i hate you? or because you can't?
i would like to add a fourth question:
- is or isn't 0.(3) = 1/3 ?
answer them without contradicting yourself (and without talking about something as unrelated as "functions") and you're done. okay?
if you instead prefer to talk about everything OTHER than these three or four questions, i believe we both can agree that i am right and you are wrong. and, last but not least, for this reason: before you start making fun of anybody's english (mine, rae's, ...), better learn maths. because actually right now you are giving a rather ridiculous show. and, as intergamer chose to say, you better aren't serious about this.