It would be awesome if somehow, someday, the final post in that thread just read “1”.
Personally, I’m looking forward to the 30-page GQ thread about whether 1.999… = 2.
Don’t forget he also quoted Led Zeppelin!
I don’t get what you’re saying.
Does 1/3 plus 1/3 plus 1/3 ***not ***= 1?
Sure it does[Sup]*[/Sup].
I think he’s referring to a particular cyclic pattern in this discussion. Proofs are given that .999… = 1, proofs are not accepted, somebody helpfully points out proofs based on .333… = 1/3, and that equivalency gets rejected.
It’s about the destination, man, not the journey.
Seriously, this is the best, most succinct, and most satisfying to my non-mathematician brain I’ve ever seen.
It makes it kinda like a question of language and defined terms; the intuitive part of my brain that wants to say “but what about a TEEENY TINY number between .999… and 1?” can just relax.
No, it does – but the post I was quoting was in reply to a post by Velocity explaining that another way of writing “1/3 + 1/3 + 1/3 = 1” is “0.3̅̅̅̅ + 0.3̅̅̅̅ + 0.3̅̅̅̅ = 0.9̅”. So bobot was implicitly denying that 0.333… is the decimal expansion of 1/3!!!
Hence my continued horror that even a pit thread I started to bitch about well-meaning but futile efforts to educate the uneducatable has turned into yet another example of the very thing I was bitching about.
Don’t mind me, I’ll just be in the corner, sobbing.
rofl, okay, I get it now.
Oh, and I also see that the last post I was quoting was also by you, Velocity. Sorry, it’s hard to read usernames with all these bitter tears of frustration in the way. 
And back in the original thread, Young Master 7777777 was insisting that it is wrong to insist that there can be a valid decimal representation for 1/3.
I didn’t deny that 1/3 can be expressed as .333. I stated that 1/3 , 3 times, is 3/3. (Which is 1, a number greater than any number beginning with a decimal. )
Jesus H. Fucking Tapdancing Christ on a Pogostick with Snot Dripping out of His Almighty Nose.
Except 0.999…
It cannot. It can be represented as “.333…” if you like. Or with a cute li’l line over the last three.
But the ellipses are important. Shit means things.
False, wrong, and also incorrect.
So, I declawed my cat the other day…
(ETA: No, not seriously, and not exactly trolling. There was a Cracked article about subjects that lead to lengthy and acrimonious debates. Declawing cats, circumcision, tipping etiquette, and the .999… debate were all on the list.)
First of all, 1/3 is equal to 0.333…, not 0.333. (the dots are important.)
Here’s the problem with your line of reasoning:
The real numbers are not discrete. They’re smooth. For any two real numbers a and b, if a ≠ b, then there is a number between a and b.
This is not friedo’s postulate; it’s part of the definition of the real numbers. Here’s an example. Let’s consider a = 3 and b = 4.
Is there a number between them? Yes, 3.5. So 3 ≠ 4.
How about 3.5 and 4? Yes, there’s 3.75. So 3.5 ≠ 4. 3.75 and 4? Sure, there’s 3.875. And so on.
We can do this forever, and if two numbers are unequal, we can always point to a number between them.
So is there a number between 0.999… and 1? If so, what is it?
If there isn’t a number between them, then 0.999… must be 1.
This is how real numbers work.
Now, it’s perfectly fine to say that you want to work with other kinds of numbers, and in those other kinds of numbers, maybe 0.999… is not the same thing as 1. But if you’re going to do that, you have to be very clear up front and say that you’re talking about some other kind of number, and not the standard real numbers. Because real numbers are what people are used to, and that’s the default assumption And there are in fact other kinds of numbers which have internally consistent rules and are actually useful for some things.
But in the real numbers, it is incontrovertibly true that 0.999… = 1. Not because some jackass decided it was true back when they were inventing numbers, but because it is a consequence of the rules of arithmetic that govern the mathematics of real numbers.
Beautifully written, elegantly expressed, absolutely true, unarguably factual…
But, you know, I’ll bet my farm and all my cattle that it won’t persuade those who don’t agree.
This is both entirely true and entirely contrary to the statement of yours I initially responded to.
To return (against my better judgement) to this topic, here is one of my peeves with this post. (And, like a metafictional literary device in a Borges story, I am beginning to see all instances of this post in this infinite discourse as the same post).
It’s technically correct (the best kind of correct) to say that you can define other notations and other numbering systems if you want to. And it’s probably true that people should understand that things like fields and groups and categories (and the notations used to describe them) are just tools, and that many tools can be devised and used for different purposes.
But the frustrating (and perhaps intractable) problem is that telling this to a crank merely gives them an “out” – it allows them to armor their fundamental misunderstanding with a misapprehension of licensure. They’ll see it as an opportunity to continue believing that they know better than anyone else. “After all,” they say to themselves, “even the arrogant ivory tower mathematicians admit the possibility of other numbers. How clever I am to see them!” And then the discussion begins anew, using slightly different words, because they don’t actually understand how to discuss things at that level of abstraction.
Nothing against your message, friedo, of course; I’m just not sure it’s possible to phrase that in a way that will actually penetrate willful ignorance.