- #71
Organic
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Hi russ_watters,
Please show me what have you found in my work, which is not self-consistent.
Thank you.
Organic
Please show me what have you found in my work, which is not self-consistent.
Thank you.
Organic
1.000...1 is not self consistent. We've been over this before though - there can't be an infinite amount of zeros before the 1 by the definition of infinity.Originally posted by Organic
Hi russ_watters,
Please show me what have you found in my work, which is not self-consistent.
Thank you.
Organic
R12 said:Okay, so in theory, .999... = 1. This could mean that .888... = 1 as well.
R12 said:Is "bumping" (posting on threads that haven't been posted on in a while) allowed here? Didn't find it in the rules.
Okay, so in theory, .999... = 1. This could mean that .888... = 1 as well.
R12 said:Is "bumping" (posting on threads that haven't been posted on in a while) allowed here? Didn't find it in the rules.
Okay, so in theory, .999... = 1. This could mean that .888... = 1 as well. After all, it is only .111... different.
No, you have simply misunderstood everything that was said here.But wait, .111... supposedly equals 1, so .888... would be 1 (.999..., to clarify.) minus 1 (.111...) But wouldn't that be zero?
As anyone who has taken basic Calculus or precalculus knows, [itex]\lim_{x\to 1} x= 1[/itex] so it is NOT "less than 1".Also, he just asked how to represent the greatest number less than 1, not if .999... was a real number. So it seams as if
lim x
x-->1
was the answer, as PrudensOptimus said.
Forgive me if I'm wrong. Trying to wrap my head around this is hard, considering I am only 16.
camilus said:This question is rather simple, you just have to be more precise.
Analyze "What is the largest number less than 1?" in terms of set theory, you can't go wrong. Greatest number less than 1 in:
1. N? none because 1 is the smallest element in the set N.
2. Z? 0
3. R? none because the set of Reals is uncountable.
n.karthick said:What about in the set of rational numbers Q which is countable
camilus said:[tex]\mathbb{Q}[/tex] is a densely ordered set, which means that for any x and y such that x < y, the exists a z in [tex]\mathbb{Q}[/tex] where x < z < y. So there in no greatest number less than 1 because whatever number x you give me when y=1, I can always find a z.
dalcde said:If you use hyperreal numbers, it might make sense that the largest number is (1-epsilon), where epsilon is an infinitesimal. However, according to my understanding, there isn't a one unified infinitesimal. An infinitesimal can be smaller than another in some weird sense.