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Alright feel free to call me a retard if you like.
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You are currently reading a thread in /sci/ - Science & Math

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?
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>>7794697
>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 1...
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>>7794697
The interval [0,1) has no maximal value. That's essentially the mistaken assumption you're making. Infinitely close to 1 is 1 and the interval does not contain it.
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0.999... is a hypothetical number that is not contained in the set [0,1)
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it seems like semantics..
.9999 only equals 1 if it continues forever..
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>>7794697

the sup of the set is 1, that's just how lub's are defined
max =/= sup, as >>7794716 said, the set has no max
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>>7794697

This is all notational semantics. You need to recognize the boundaries of mathematics as a language to describe real things.
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>>7794716
oh fuckin duh ok that clears it up. i figured i was wrong but i wasnt exactly sure where it was.