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2016-01-19 04:24:41 Post No. 7794697
Post No. 7794697
Alright feel free to call me a retard if you like.
I'm in an intro to analysis course, and we've looked at intervals, and maxima / minima. Answer me this: If it is accepted that 0.9999... and 1 represent the same number. Now, consider the open ended interval [0,1). Then, any x in this interval will be 0 <= x < 1. So can x be equal to 0.9999... since there will be no maximum for this interval? In other words, we can get infinitely close to 1 but never arrive at one. The best approximation of "infinitely close to 1" is 0.9999..., but this is known to represent the same number. So logically x cannot be 0.9999... as it violates the interval. So then what is the approximation of "infinitely close to 1" in this case? Or am I totally off base here?