RE: By the way, 0.999... = 1
November 3, 2011 at 2:42 pm
(This post was last modified: November 3, 2011 at 2:42 pm by edk.)
(November 3, 2011 at 11:00 am)IATIA Wrote:(November 3, 2011 at 9:02 am)edk141 Wrote:
You cannot use infinities in algebra and a repeating decimal falls into the infinity category. In calculus infinities are calculated as limits. As in "approaching 1", but does not equal one. Infinities are strange and do not conform to our mathematics. A piece of infinity is still infinity. Two infinities are not twice as big as one infinity. One cannot calculate an infinite progression because that would take an infinite amount of time, but through calculus, we can calculate the limit. Like I said though, it is accepted as 1 because the definition of numbers states that between any two real numbers there is another real number. So technically, 0.999... is not even a real number. (then again, maybe 1 is the unreal number )
1. It's not infinite, it just has an infinite number of digits.
2. Algebra does deal with infinite things sometimes. Finding the sum of infinite series, for example.
3. 0.999... is just a representation of a number.
I'll try to demonstrate it to you with a different rational number:
The decimal representation of 22/7 is infinitely long. It looks like this:
3.(142857)...
The number one million times larger than that is 3142857.(142857)...
The number 999999 times larger than 22/7 is 3142857.142857... - 3.142857... = 3142854 exactly. 3142854/999999 = 22/7.