Infinity = 1?

[Maze1125]

But, while we're on the subject of things equalling 1:
0.999... = 1

GRRRRRRRR... I disagree.
Goddamn decimals. A fraction sees past all this bullshit and actually divides 1 by an exact third, not by a 'infinity plus 1' style number that mathematicians just pass off as 0.999... .

There's no "passing off" involved.
0.999... has a precise definition and it can be easily shown from that definition that it equals 1.
0.333... also has a precise definition and is exactly equal to the fraction 1/3.
Fractions certainly look neater on the page, but that doesn't mean they are less exact.

You completely missed my point. Fractions are MORE precise, because they don't get into this whole shitty business. As far as fractions are concerned, it's just 1/3.

No, you completely missed my point.
Just because you don't like the notation of decimals, does not make them less precise. Nicer to write perhaps, but not less precise.

Also, I didn't realise that "shitty business" was a mathematical term.

And I will never agree that 9 = 10.

That's good, because 9 doesn't equal 10.
But 0.999... still equals 1.

 

[Davey Woo]

I thought that infinity was an incomprehensible number.
So I think everyone should stop trying to comprehend something that we cannot comprehend.

 

[Lexodus]

But, while we're on the subject of things equalling 1:
0.999... = 1

GRRRRRRRR... I disagree.
Goddamn decimals. A fraction sees past all this bullshit and actually divides 1 by an exact third, not by a 'infinity plus 1' style number that mathematicians just pass off as 0.999... .

There's no "passing off" involved.
0.999... has a precise definition and it can be easily shown from that definition that it equals 1.
0.333... also has a precise definition and is exactly equal to the fraction 1/3.
Fractions certainly look neater on the page, but that doesn't mean they are less exact.

You completely missed my point. Fractions are MORE precise, because they don't get into this whole shitty business. As far as fractions are concerned, it's just 1/3.

No, you completely missed my point.
Just because you don't like the notation of decimals, does not make them less precise. Nicer to write perhaps, but not less precise.

Again, missing the point. With fractions, there is no controversy. It is just 1/3; exactly 1/3, no more, no less. Decimals do not have that luxury, hence this argument.

Also, I didn't realise that "shitty business" was a mathematical term.

I didn't realise that you're an idiot. Shame on me, huh?

And I will never agree that 9 = 10.

That's good, because 9 doesn't equal 10.
But 0.999... still equals 1.[/quote]
No, it doesn't. It equals 0.999... . It will never be exactly 1. in the same way that 0.9 is not 1, 0.99 is not 1, 0.999 is not 1...

 

[Maze1125]

But, while we're on the subject of things equalling 1:
0.999... = 1

GRRRRRRRR... I disagree.
Goddamn decimals. A fraction sees past all this bullshit and actually divides 1 by an exact third, not by a 'infinity plus 1' style number that mathematicians just pass off as 0.999... .

There's no "passing off" involved.
0.999... has a precise definition and it can be easily shown from that definition that it equals 1.
0.333... also has a precise definition and is exactly equal to the fraction 1/3.
Fractions certainly look neater on the page, but that doesn't mean they are less exact.

You completely missed my point. Fractions are MORE precise, because they don't get into this whole shitty business. As far as fractions are concerned, it's just 1/3.

No, you completely missed my point.
Just because you don't like the notation of decimals, does not make them less precise. Nicer to write perhaps, but not less precise.

Again, missing the point. With fractions, there is no controversy. It is just 1/3; exactly 1/3, no more, no less. Decimals do not have that luxury, hence this argument.

There is no controversy, every single mathematician knows that 0.999... = 1 and that 0.333... = 1/3.
The only people who argue are people who don't understand the foundations of mathematics.

Also, I didn't realise that "shitty business" was a mathematical term.

I didn't realise that you're an idiot. Shame on me, huh?

Says the guy who can't successfully reformat quote tags...

And I will never agree that 9 = 10.

That's good, because 9 doesn't equal 10.
But 0.999... still equals 1.

No, it doesn't. It equals 0.999... . It will never be exactly 1. in the same way that 0.9 is not 1, 0.99 is not 1, 0.999 is not 1...

Okay then, if you're so sure you're right, please define 0.999... for me.
Because you can't be sure that it's not 1 if you aren't even sure what it is.

 

[JMV]

I REALLY dislike when people mix Math theory and Philosophy, sometimes. Wait, most times.

 

[Blackhol]

Easy, each infinite universe houses infinitely, infinite other galaxy's with an infinitive amount of other infinite universe than span an infinite space, which is also infinite

 

[The_root_of_all_evil]

My usual response to this and most religious situations.

Finite minds cannot comprehend the infinite. That's where most of the problem lies and why space is big, like really big. I mean you may just think it's a long way down to the shops but that's peanuts compared to (infinite) space...

 

[Maze1125]

Blah blah blah all that noise.

Alright, fuck this. If you can't have an argument without being a condescending asshole, there's no point trying. Fuck this, fuck you, and goodnight.

And, for the record, what the fuck were you babbling about quote tags for?

You outright call me an idiot, and yet I'm the "condescending asshole" for responding?
Aren't you a lovely person...

Anyway, I'm guessing that outburst was just to avoid defining 0.999... because when I asked you to do that you realised you couldn't do it because you didn't even understand the concept you were arguing about.

 

[Outright Villainy]

(any number)/0 is infinity. well, the neatest way I can think of expressing an abstract notion that has no real value.

It's fun thinking about an infinite universe with finite matter, because it makes so little sense and my brain hurts. And we live in an expanding universe that's accelerating in it's expansion, so there's even less matter going around! Also, finite matter in an infinte universe means that the density of matter in the universe is 0, and therefore THERE IS NO MATTER.

Also, 0.999* is 1. Funny if you talk in fractions it's a lot easier to convince someone.
1/3=0.333* for example, does that mean 0.333*=/=1/3? Our entire basis of maths would break down!

Also, off topic, does anyone else get annoyed when imaginary numbers are used in physical equations (god damn you euler!), particularly waves. I like physics because it can be shown, and thought through logically, and imaginary numbers in equations just fucks that up for me!

 

[Maze1125]

(any number)/0 is infinity.

Provided the numerator isn't 0.

I like physics because it can be shown, and thought through logically, and imaginary numbers in equations just fucks that up for me!

Don't try Quantum Mechanics then.

 

[Outright Villainy]

Don't try Quantum Mechanics then.

I do quantum mechanics actually. It's pretty much the defintion of counter-intuitive in many aspects. The single photon beam showing interference patterns is a great example.
Also, stop being so nitpicky and presumptious.

 

[fun-with-a-gun]

also. just because I gave my friend a headache with this oone before.....consider a 1-dimensional square...

That's a line.

you're all wrong. it's less then a dot.

 

[newfoundsky]

We could accept that space is NOT infinite.

 

[Maze1125]

Don't try Quantum Mechanics then.

I do quantum mechanics actually. It's pretty much the defintion of counter-intuitive in many aspects. The single photon beam showing interference patterns is a great example.
Also, stop being so nitpicky and presumptious.

When it comes to mathematics you have to be "nitpicky". It's often the difference between being right and being wrong, especially when it comes to counter intuitive things.

There have been huge numbers of mistakes in this thread, but I've ignored them because they weren't aimed directly at me and people often take offence. I responded to your one because you seemed like the sort of person who recognised the importance of such precision and could cope with being slightly corrected so that others reading could read the exact answer and perhaps one or two might even have seen the importance of precision for themselves.

I guess you proved me wrong there.

Further, I wasn't even being anywhere near as "nitpicky" as a could have been.
What I ought to have said was this:
"Actually, that is only true in number sets where infinity is defined as a number, in sets without infinity, such as the Real Numbers, it is not true. In fact, sometimes you can have a set that includes infinity but that equality is still not true, for example the Real Numbers united with both infinity and negative infinity.
Also, in the sets where it does hold, it only holds if the numerator is a number other than 0."

Lastly, that comment about QM was a joke, you know as in "You don't like complex numbers or concepts that can't be thought through logically? You'd better not try the discipline that takes place entirely in complex Hilbert spaces and is almost completely unintuitive then. Ha ha!"

 

[Pokeylope]

Loud noises!

Monty Python can explain it all [http://www.youtube.com/watch?v=buqtdpuZxvk]

exploding space vagina warning

 

[FallenJellyDoughnut]

One is the loneliest number that you'll ever do
Two can be as bad as one
It's the loneliest number since the number one

No is the saddest experience you'll ever know
Yes, it's the saddest experience you'll ever know
`Cause one is the loneliest number that you'll ever do
One is the loneliest number, worse than two!

 

[FallenJellyDoughnut]

One of the parts which gets me:
Infinity - infinity = infinity.

That's not actually true. They covered it in the program.

Infinity + Infinity = Infinity

Infinity - Infinity = 0 or Infinity

I technically, it could in fact become other finite numbers too. It's all very confusing with Infinity subtraction.

Because you can have different sizes of Infinity. Interestingly, Infinitys can be larger than each other. Decimal Infinity has been proven to be larger than Integer Infinity.

They also had lots of stuff there about the Infinite Hotel problem too.

Good program that was.

How the hell can INFINITY be larger than another INFINITY?! ITS UNLIMITED! IT NEVER STOPS! ITS GOD DAMN FUCKING HUGE!!! *Brain Explosion*

 

[Silver]

It works out if you're a computer. Infinity = 1 with infinity being a statement, and 1 being true. So, in a sense, with 1 representing true, it works out. But other than that, no, not really. Sorry.

 

[Joshimodo]

1 is a defined digit and bedrock for all of mathematics. It's also a concept.


Infinity, however, is purely a concept. It's endless, and utterly impossible to imagine. It's not "all of X thing", as that would still be a number. Trying to think of infinity is futile, much like imagining the 4th dimension.

 

[lodo_bear]

0/0 = ?
Infinity - Infinity = ?
Infinity/Infinity = ?
Infinity*0 = ?

I mention these because all of these relations are undefined. They can equal anything; the only time they have a precise value is when they are given context.

Take the equation X/X, for example. For any regular number, it is visibly equal to 1, whether that number is Pi, 42, 47, over 9000, 1.21 billion, or what have you. It keeps on being 1 no matter how big or how small X is, so we can infer that when X = 0 or X = Infinity, X/X still equals 1.

However, what happens when we have (e^X)/X ? As X goes to Infinity, e^X also goes to Infinity, so we have Infinity/Infinity again, but e^X approaches Infinity much faster than X does, so when X = Infinity, (e^X)/X also equals Infinity.

Infinity is like a regular number in many respects, but it's hard to work with in many ways.

Trying to think of infinity is futile, much like imagining the 4th dimension.

Imagining the fourth dimension isn't that hard. It's just time, after all.
Now, imagining a fourth spatial dimension...that warps your brain.

But 0.999... still equals 1.

No, it doesn't. It equals 0.999... . It will never be exactly 1. in the same way that 0.9 is not 1, 0.99 is not 1, 0.999 is not 1...

In case you don't like the (rather elegant) proof that Lexodus provided, here's another.

X = 0.999...etc.
X*10 = 9.999...
X + 9 = 9.999...
X*10 = X + 9
9*X = 9
X = 1

Think about it like this: the difference between 0.9 and 1 is 0.1, the difference between 0.99 and 1 is 0.01, and so on. What happens when you have an infinite number of nines after the decimal point? There's nothing you can add to it to make it 1. Can you have 0.00...(infinite number of zeroes)...1? You can try to make such a number, but it will be equal to 0, since all those infinite zeroes after the decimal point push that 1 into oblivion. So, in order to increase 0.999...etc. to 1, you must add zero to it, and if the difference between any two numbers is zero, they are perfectly equal. QED.