## Search found 54 matches

Wed Mar 22, 2017 2:53 pm
Forum: Logic and Philosophy of Mathematics
Topic: Is 0.9999... really the same as 1?
Replies: 117
Views: 12698

### Re: Is 0.9999... really the same as 1?

Not sure of your point? As in reality Homer reaches the end of the path. Do any of these wiki points apply to how you think about this? "Students of mathematics often reject the equality of 0.999… and 1, for reasons ranging from their disparate appearance to deep misgivings over the limit concept a...
Wed Mar 22, 2017 8:10 am
Forum: Logic and Philosophy of Mathematics
Topic: Is 0.9999... really the same as 1?
Replies: 117
Views: 12698

### Re: Is 0.9999... really the same as 1?

... I wouldn't assume 0.999... is 1 merely because 0.999... approaches it. Defining something as equal does not change the reality of whether they are equal. What's 0.999... in reality? This Zeno's paradox is the equivalent problem in the binary number system Suppose Homer wishes to walk to the end...
Wed Mar 22, 2017 2:36 am
Forum: Logic and Philosophy of Mathematics
Topic: Is 0.9999... really the same as 1?
Replies: 117
Views: 12698

### Re: Is 0.9999... really the same as 1?

I was interested in the later bits on skepticism and the alternative number systems where it doesn't equal 1. Oh I see. Well this fits in with something I keep saying. If we defined the symbol .999... to mean 47, then since 47 is different than 1, it must be that .999... ≠ 1. Of course all these al...
Sat Mar 18, 2017 12:49 pm
Forum: Logic and Philosophy of Mathematics
Topic: Is 0.9999... really the same as 1?
Replies: 117
Views: 12698

### Re: Is 0.9999... really the same as 1?

0.1 < 0.2 < 0.3 < 0.4 < 0.5 < 0.6 < 0.7 < 0.8 < 0.9 < 0.99 < 0.999 < 0.9999 all have a units digit of 0, all are less than one. All real numbers with a units digit of 0 are less than one. 0.9999... < 1 It's over '<' changes to '<=' in the limit. You need to get your money back from whoever taught y...
Sat Mar 18, 2017 3:20 am
Forum: Logic and Philosophy of Mathematics
Topic: Is 0.9999... really the same as 1?
Replies: 117
Views: 12698

### Re: Is 0.9999... really the same as 1?

Am I required to weigh in here? Surreals, ok. This looks promising Promising what? I confess I'm at a loss to follow your point. Promising a dramatic refutation of the previous two centuries of math? I'd say you've done no such thing. Perhaps if you stated a clear thesis or argument, we could analy...
Fri Mar 17, 2017 5:15 am
Forum: Logic and Philosophy of Mathematics
Topic: Is 0.9999... really the same as 1?
Replies: 117
Views: 12698

### Re: Is 0.9999... really the same as 1?

This looks promising https://www.youtube.com/watch?v=aRUABAUcTiI http://mathworld.wolfram.com/SurrealNumber.html Like with the hyper-reals I have not looked into the surreal numbers before much either. But according to this, 0.9999... and 1 are different values within the Surreal number system.
Tue Mar 14, 2017 6:52 pm
Forum: Logic and Philosophy of Mathematics
Topic: Is 0.9999... really the same as 1?
Replies: 117
Views: 12698

### Re: Is 0.9999... really the same as 1?

I found another video about 0.999... = 1. I'm guessing wtf will like this better since they say it equals 1 at the end https://www.youtube.com/watch?v=rT1sIVqonE8
Tue Mar 14, 2017 11:43 am
Forum: Logic and Philosophy of Mathematics
Topic: Is 0.9999... really the same as 1?
Replies: 117
Views: 12698

### Re: Is 0.9999... really the same as 1?

... In a "2+2" thread I would break down the thought process that goes into convincing someone that it is the same as 4. The law of identity and the law of non-contradiction would come up. ... Sorry, I'm loving this thread as whilst I can understand very little of it I'm enjoying the little philoso...
Tue Mar 14, 2017 12:55 am
Forum: Logic and Philosophy of Mathematics
Topic: Is 0.9999... really the same as 1?
Replies: 117
Views: 12698

### Re: Is 0.9999... really the same as 1?

Excerpt from a conversation I recently had in my head: Imaginary You: Thank you so much, wtf, for taking the time and trouble to write out that clear explanation of the mathematical argument that .999... = 1. It's better than anything in my dark and fuzzy real analysis book, and way more understand...
Mon Mar 13, 2017 5:49 pm
Forum: Logic and Philosophy of Mathematics
Topic: Is 0.9999... really the same as 1?
Replies: 117
Views: 12698

### Re: Is 0.9999... really the same as 1?

So humor me. Talk about the law of identity with respect to 2 + 2 = 4, and how it does or does not fall victim to the exact same criticism you leveled at .999... = 1. Correct, I was thinking 1 was not also a representation of a real number when I said that. The point though is if any property disti...
Mon Mar 13, 2017 1:43 am
Forum: Logic and Philosophy of Mathematics
Topic: Is 0.9999... really the same as 1?
Replies: 117
Views: 12698

### Re: Is 0.9999... really the same as 1?

Based on this earlier statement you made in a previous post I'm assuming you agree with me on some level. I will accept your concession if you are done here, here's what you said again: Please note that I made no claim that .999... = 1 is true. I only say that it's a valid derivation from a set of a...
Sun Mar 12, 2017 6:17 am
Forum: Logic and Philosophy of Mathematics
Topic: Is 0.9999... really the same as 1?
Replies: 117
Views: 12698

### Re: Is 0.9999... really the same as 1?

It's not a real numbers or nothing problem. Perhaps, but as a divide-and-conquer strategy it's vital to nail this down for the real numbers before going off to other interpretations. You are clear that you don't accept the real number interpretation. That's fine, if you have more points to make abo...
Sat Mar 11, 2017 10:21 pm
Forum: Logic and Philosophy of Mathematics
Topic: Is 0.9999... really the same as 1?
Replies: 117
Views: 12698

### Re: Is 0.9999... really the same as 1?

I don't know if 0.9999... is a real number. If you don't believe in the real numbers, even as a meaningless formal axiomatic system as described in your real analysis book, there's nothing to discuss. It's not a real numbers or nothing problem. Rules are subject to change. Decimals are a representa...
Sat Mar 11, 2017 4:09 pm
Forum: Logic and Philosophy of Mathematics
Topic: Is 0.9999... really the same as 1?
Replies: 117
Views: 12698

### Re: Is 0.9999... really the same as 1?

Without getting too involved in the semantics of hyperreals, they do allow us to demonstrate a difference between 0.99999... and 1. The distinction is between limit and st(limit) if I read it correctly the limit of the sequence 0.9, 0.99, 0.999, ... is less than 1 in the hyperreals whereas the st(l...
Sat Mar 11, 2017 5:10 am
Forum: Logic and Philosophy of Mathematics
Topic: Is 0.9999... really the same as 1?
Replies: 117
Views: 12698

### Re: Is 0.9999... really the same as 1?

I skimmed the Better Explained piece. It seems like a compendium of all the wrong and misleading things people say on these .999... discussion forum threads. In particular, the author claims that .999... < 1 in the hyperreals. This is simply not only false, but provably impossible . Professor Amit ...