[QUOTE=Smashmaster;35298671]Okay, let me represent 1 in a different way.
2/2
It's represented in a different way, therefore it must be a different number! Wrong.
How about 10-9?
Are we going to argue that 10-9 =/= 1?[/QUOTE]
This person has the right idea. Central to understanding the problem is understanding the concept that written numbers are just symbols that represent a value. Since 0.999... is written differently than 1, most people assume that they are not equal. However, although they are represented differently, they are equivalent to the same value, in the same way that 3/4 and 0.75 represent the same value. It's an issue of notation, not of approximation.
[QUOTE=Mr. Sun;35297817]So basically round up...
Who cares THIS MUCH about math.[/QUOTE]
No, it's not a round up. 0.9... is a decimal representation of 1/3 * 3. 3/3 = 1, therefore 0.9... = 1.
[QUOTE=gamefreek76;35298699]No matter how infinitesimal it gets, it still does not equal exactly 1.[/QUOTE]
You apparently don't know what infinite means.
[QUOTE=gamefreek76;35298699]No matter how infinitesimal it gets, it still does not equal exactly 1.[/QUOTE]
[url=http://en.wikipedia.org/wiki/Zeno's_paradoxes]This is mathematics, not philosophy.[/url]
You can't think of numbers as being so "literal". Numbers are a representation of something. In a practical sense, if you are multiplying 0.3... * 3, you are multiplying a third by three. In practicality it would equal one whole, even though the decimal representation would say that it is < 1. The decimal representation just comes up with that because of the way you multiply.
If this is truly confusing, then I would hate to see you learning irrational numbers. Pi and Square Root of 2 will fucking boggle your mind, man.
[QUOTE=john_pelphre;35298765][url=http://en.wikipedia.org/wiki/Zeno's_paradoxes]This is mathematics, not philosophy.[/url][/QUOTE]
That may be the problem.
I read up on it and was still not compelled enough to believe it. It just seems like a cop out to me.
Maybe one day I'll be convinced, but not today.
I think it may be due to the thinking of a philosopher versus a mathematician; both are trying to explain an idea, though the former is less compelled with simple representation. Mathematicians only need a place holder for their ideas that follow a concurrent pattern. A philosopher needs more meaning to the situation than a simple definition. He needs everything that defines that, and Ad infinitum.
[QUOTE=gamefreek76;35298699]No matter how infinitesimal it gets, it still does not equal exactly 1.[/QUOTE]
Oh look, a post saying the same damn thing for the fiftieth time. Allow me to post this again:
[t]http://filesmelt.com/dl/0.999_1_.jpg[/t]
[url]http://en.wikipedia.org/wiki/0.999...#Algebraic_proofs[/url]
[b]Infinity does not exist in this context.[/b] If it is infinitely close to one, then it is one. This is not a hiccup in the law of mathematics, it's just how our numerical system works. Refer back to this post:
[QUOTE=calzoneman;35298730]Central to understanding the problem is understanding the concept that written numbers are just symbols that represent a value. Since 0.999... is written differently than 1, most people assume that they are not equal. However, although they are represented differently, they are equivalent to the same value, in the same way that 3/4 and 0.75 represent the same value. [b]It's an issue of notation, not of approximation.[/b][/QUOTE]
[QUOTE=yawmwen;35298735]No, it's not a round up. 0.9... is a decimal representation of 1/3 * 3. 3/3 = 1, therefore 0.9... = 1.[/QUOTE]
plus
(1/3 * 3) = (.333... * 3) = (.999...) = ((1/3) * 3) = ((1*3)/3) = (3/3) = 1
For us engineers .99.....=1 is simply true because it's close enough.
1/3 =/= 0.333333
1/3 = 0.333333 to infinity.
0.3333333 etc. is used to represent 1/3. There's a reason why a lot of people just round up to 0.3333334.
[QUOTE=Dr. Evilcop;35298915]If it is infinitely close to one, then it is one.[/QUOTE]
Infinitely close to one [b]but not one[/b]
Are we just thinking of different numbers or something?
[QUOTE=Paramud;35299849]Infinitely close to one [b]but not one[/b]
Are we just thinking of different numbers or something?[/QUOTE]
You guys are talking about the same number. You are just wrong. Something cannot be infinitely close to something. That isn't how infinity works.
In fact, the whole idea of there being a number 0.3... is flawed. It's literally the way to write a number that you can't write out in decimal form. 0.3... it's just a representation of 1 divided by 3. If you follow that logic, then 0.9... is literally just a decimal representation of 3 divided by 3. Do some basic arithmetic and 3 divided by 3 is 1. It's very simple.
[QUOTE=Paramud;35299849]Infinitely close to one [b]but not one[/b][/QUOTE]
[b]YOU WERE JUST GIVEN AN EXACT MATHEMATICAL PROOF THAT IT IS EXACTLY THE SAME AS ONE.[/b]
Unless you can prove that convergence theorem is somehow utterly and completely false, you are wrong. You are literally arguing that 1 somehow doesn't equal 1.
[QUOTE=Watevaman;35293458]The people that rate OP dumb have never taken higher level math classes.[/QUOTE]
Or they think that these threads are completely unnecessary.
Math is so interesting, just like with line that gets infinitely closer to the y or x axis, but never touches it. I can't remember the name of it for the life of me.
[editline]26th March 2012[/editline]
[QUOTE=paul simon;35300115]Or they think that these threads are completely unnecessary.[/QUOTE]
So they come and read it on their own free will even after knowing what the thread encompasses by reading the title JUST so they can rate it dumb? I believe there's a word for people like that, but I'll play nice.
[QUOTE=Dwinnon;35300121]Math is so interesting, just like with line that gets infinitely closer to the y or x axis, but never touches it. I can't remember the name of it for the life of me.
[/QUOTE]
Asymptote
0.333... x 3 = 1
0.999... = 0.999...
[QUOTE=Glorbo;35300135]Asymptote[/QUOTE]
Thanks, I've been out of school way too long, its hard to retain any of that shit.
Why do 12 year olds think they know more than Euler did?
why couldnt this thread be posted in mass debate
it would make a good thread
[QUOTE=Death_God;35300364]why couldnt this thread be posted in mass debate
it would make a good thread[/QUOTE]
I just realized that in an English accent, "mass debate" almost sounds like "masturbate"
[QUOTE=Death_God;35300364]why couldnt this thread be posted in mass debate
it would make a good thread[/QUOTE]
Because there would be no proper debate, it's a mathematical fact. The thread will just have people that have a decent enough understanding of limits and infinity arguing against those that don't.
Case in point:
[QUOTE=Death_God;35300457]oh for fucks sake
if 0.999 = 1
what would 0.555 equal?[/QUOTE]
oh for fucks sake
if 0.999 = 1
what would 0.555 equal?
[QUOTE=Death_God;35300457]oh for fucks sake
if 0.999 = 1
what would 0.555 equal?[/QUOTE]
0.555 = 555/1000
0.555... (with the ellipsis after it) = 5/9
so if 0.555 is an infinite number, it would still equal the same as 5/9
so what makes 0.999 any different?
if anything it's just rounded to 1
because with the logic that 0.999 = 1 would mean that 0.599 would equal 0.6, 0.699 = 0.7, etc.
[QUOTE=Death_God;35300490]so if 0.555 is an infinite number, it would still equal the same as 5/9
so what makes 0.999 any different?
if anything it's just rounded to 1
because with the logic that 0.999 = 1 would mean that 0.599 would equal 0.6, 0.699 = 0.7, etc.[/QUOTE]
You're not quite getting it.
For one, 0.555 does NOT equal 5/9. 0.555 equals 555/1000. 0.5... is the same as writing 5/9.
And there is no difference, the whole point of this is that 0.9... is exactly the same as writing 3/3, which is equal to 1. 0.5... or 0.3... or 0.9... are all ways of writing a specific FRACTION number.
And no, you don't just "round up" the numbers. I'll explain it again. If 0.3... is the same as 1/3, and 1/3 times 3 is the same as 1, then 0.3... HAS to be equal to 1. There is absolutely NO way you can argue against that unless you want to argue that 0.3... is NOT 1/3.
[QUOTE=Death_God;35300490]because with the logic that 0.999 = 1 would mean that 0.599 would equal 0.6, 0.699 = 0.7, etc.[/QUOTE]
As long as the 9s are repeating.
[quote=Wikipedia] The result that 0.999... = 1 generalizes readily in two ways. First, every nonzero number with a finite decimal notation (equivalently, endless trailing 0s) has a counterpart with trailing 9s. For example, 0.24999... equals 0.25, exactly as in the special case considered. These numbers are exactly the decimal fractions.[/quote]
[URL]http://en.wikipedia.org/wiki/0.999...#Generalizations[/URL]
[QUOTE=yawmwen;35300530]You're not quite getting it.
For one, 0.555 does NOT equal 5/9. 0.555 equals 555/1000. 0.5... is the same as writing 5/9.
And there is no difference, the whole point of this is that 0.9... is exactly the same as writing 3/3, which is equal to 1. 0.5... or 0.3... or 0.9... are all ways of writing a specific FRACTION number.
And no, you don't just "round up" the numbers. I'll explain it again. If 0.3... is the same as 1/3, and 1/3 times 3 is the same as 1, then 0.3... HAS to be equal to 1. There is absolutely NO way you can argue against that unless you want to argue that 0.3... is NOT 1/3.[/QUOTE]
you pretty much took my entire post too literal
i obviously didn't mean 0.555 up to the thousandths place, i meant 0.555 as a repeating decimal
and see i honestly don't see how 0.999 = 1 ISN'T rounding.
it's no different from how rounding 0.55 could be 0.6, it's no different from that at all.
[QUOTE=Death_God;35300562]you pretty much took my entire post too literal
i obviously didn't mean 0.555 up to the thousandths place, i meant 0.555 as a repeating decimal[/QUOTE]
For future reference, and ease of communication. 0.555 is not the same as 0.5...
The ellipses are important, because they tell you that the 5's go on forever. 0.555 ends in the thousandths place, so that isn't really going on forever.
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