## Search found 54 matches

- Fri Mar 10, 2017 6:05 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Is 0.9999... really the same as 1?
- Replies:
**117** - Views:
**13838**

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

oh ok I only glanced at that paper myself. I prefer my more straightforward proof of 0.9999... < 1. https://betterexplained.com/articles/a-friendly-chat-about-whether-0-999-1/ explains the problems pretty good to me. I'm surprised you didn't really tackle that short proof and you seemed to shut down...

- Fri Mar 10, 2017 8:10 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Is 0.9999... really the same as 1?
- Replies:
**117** - Views:
**13838**

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

I'm still not convinced 0.9999... qualifies as a real number. If 0.9999.. and 1 do not differ by a real amount but do differ by a non-real amount, would that mean they are different? I don't know what that means. What is differing by a non-real amount? The same way it is not the case that 3 = pi in...

- Thu Mar 09, 2017 10:12 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Is 0.9999... really the same as 1?
- Replies:
**117** - Views:
**13838**

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

But when comparing 3 and Pi there exists no natural number that separates them and yet 3<Pi. As I said a couple of posts ago, the order on the rationals is derived from the order on the integers, which is derived from the order on the naturals. And then the order on the reals is derived from the or...

- Thu Mar 09, 2017 9:38 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Is 0.9999... really the same as 1?
- Replies:
**117** - Views:
**13838**

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

But you defined x<y as when x is smaller than y by some number I never did that. I noted that it's a fact. If you claim .999... is less than 1, then it must be less by some amount, which I called epsilon. You disagree? By the way I found the definition of < on Wikipedia. https://en.wikipedia.org/wi...

- Thu Mar 09, 2017 8:46 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Is 0.9999... really the same as 1?
- Replies:
**117** - Views:
**13838**

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

Where is the definition of "<"? I couldn't find one for the equal sign. Equality is defined by the axiom of extensionality. That has a Wiki page. When you define the natural numbers via the successor operation, you can define < via succession. You use that to define < on the rationals, and from tha...

- Thu Mar 09, 2017 8:43 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Is 0.9999... really the same as 1?
- Replies:
**117** - Views:
**13838**

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

...for the same reason 0.0000...1 is considered 0 as a real number. There is no such number. What on earth could it mean? Didn't I explain that a sequence is a function whose domain is the natural numbers? Why are you going down this rabbit hole? Please, get out your old real analysis book and feel...

- Thu Mar 09, 2017 8:23 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Is 0.9999... really the same as 1?
- Replies:
**117** - Views:
**13838**

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

...for the same reason 0.0000...1 is considered 0 as a real number. There is no such number. What on earth could it mean? Didn't I explain that a sequence is a function whose domain is the natural numbers? Why are you going down this rabbit hole? Please, get out your old real analysis book and feel...

- Thu Mar 09, 2017 7:30 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Is 0.9999... really the same as 1?
- Replies:
**117** - Views:
**13838**

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

I think I came up with a possible way to prove 0.9999... < 1 with limits in the real number system. Why are you devolving into this kind of discourse? If we're discussing gravity and I say, "I've found a way to prove that things fall up," you don't need to read further. Right? What's the metric on ...

- Thu Mar 09, 2017 4:49 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Is 0.9999... really the same as 1?
- Replies:
**117** - Views:
**13838**

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

I think I came up with a possible way to prove 0.9999... < 1 with limits in the real number system. Let the set Compare = { LessThan, Equals, GreaterThan } CompareReals( x, y) is a function with a domain of x and y in the set of real numbers and range in the set Compare. CompareReals(x, y) = LessTha...

- Thu Mar 09, 2017 1:45 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Is 0.9999... really the same as 1?
- Replies:
**117** - Views:
**13838**

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

I've understood everything you've said. I think he's just saying it's interesting. Within real numbers and with limits 0.9999... = 1. But on another level is 0.9999...=1 true too? Using criteria like these https://en.wikipedia.org/wiki/Criteria_of_truth I'm thinking Greta is a she but of course han...

- Thu Mar 09, 2017 5:52 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Is 0.9999... really the same as 1?
- Replies:
**117** - Views:
**13838**

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

Wtf has been doing a job on us I'm sorry, how should I take that remark? You think I'm bs-ing or flimflamming in some way? I know the mathematical side of this very well and I'm doing my best to explain it. If you think I'm "doing a job" on you I can see I should save my keystrokes. Is this a langu...

- Thu Mar 09, 2017 5:41 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Is 0.9999... really the same as 1?
- Replies:
**117** - Views:
**13838**

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

I read this over, they pretty much said all the things I've said already but probably explain it better https://betterexplained.com/articles/a- ... er-0-999-1

- Thu Mar 09, 2017 4:58 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Is 0.9999... really the same as 1?
- Replies:
**117** - Views:
**13838**

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

Any such number that is less than one cannot be 0.999.... It instead would be a finite decimal, as above, with a finite number of repeated 9s. Yes that's the proof! That's more precise than "infinitely many 9's." But if that's what you meant, then you are absolutely right! If we claim that .999... ...

- Thu Mar 09, 2017 2:53 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Is 0.9999... really the same as 1?
- Replies:
**117** - Views:
**13838**

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

With help earlier in the thread I see the situation as this: 0.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999...

- Wed Mar 08, 2017 9:53 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Is 0.9999... really the same as 1?
- Replies:
**117** - Views:
**13838**

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

Given that 0.9999... can be rewritten as lim x->infinity of f(x) where f(x) = 1 - 10^(-x) It's closer to the definition to say .999... = lim(n->infinity) of sum(1 to n) 9/10^n, but the difference isn't important for our purposes. I'll accept what you wrote. and the definition of limit being for eve...