Glad to have you on board You shouldn't feel badly about this, some similar issues troubled mathematicians for a long time. The modern convention is that 0.999... is defined as the limit of the sequence 0.9, 0.99, 0.999, 0.9999, etc., and there does not exist a number that is in any sense "infinitely close" to one without being equal to one. People have developed other number systems with numbers like this (for example, numbers smaller than any positive real number, but still greater than zero), but there is a price to be paid - specifically, some of the ordinary rules of arithmetic must be broken. It is impossible to invent such numbers without breaking at least some of the familiar rules of math.
Infinitely small and nonexisting are mutually exclusive. Something is either infinitely small or none existant.
if I/infinity = 0, then 1/infinity(infinity) = 0(infinity), then 1 = 0. right?
10x-x > 9.999... - 0.999...; It is one decimal place off. Try it in scientific notation and remember infinity -1 < infinity, it is safe to say by 1. (...) with nothing following is deceiving. Not all ifinities are created equal. Don't ask Homo bibi. He says he avoids arithmetic and from what he's written it's for the best.
1-0.999... = 0.000...1: It can only be equal to zero by mutal agreement. I offered a knowledgible agreement. You declined. Logic is apparanly not your long suite. I do not expect you to be able to understand.
If you think that real numbers are finite, you need all of the help that you can get.
0.999... Is an open ended phrase, written in a self limiting notation. It has little if any meaning. What number when subtracted from 0,999... would equal 0.999... ending with the numeral 8 instead of 9? How would you write such a number using your beloved notation? Would you contend that such a number does not exist?
0.999...9 - 0.000...1 = 0.999...8 Weeee, wasn't that fun?
Rewrite that in your limited notation. 0.999... is a trick phrase. It is used to confuse and deceive. It eliminates infinite possibilities and generates nothing but circular arguments.
Does 0.111... = 0.112... or 0.110...? What is the limit of 0.111...?
Last edited by Wayne Bruinekool; 11-22-2010 at 02:09 PM.
Hahahaha,owwwch...my brain hurts,even though that's impossible...I love paradoxes.
Your objection about the counting numbers vs. non-counting numbers would hold for 1 and 1.0 as well. I hope you would not be arguing that 1 does not equal 1.0?
I would say we can reasonably limit it to just the consideration of value. So, it seems that it is your opinion that they are equal in value then?"Is 0.999... equal to one?" is too vague for a definitive answer.