1 + 1 = ...1?
 

Ok, so a bit of back story...
About 7 years ago a friend of mine and I were having a discussion about religion. I think it was something to do with the "second coming of christ". Anyway, This got me, somehow, on the subject of math.
If there are an infinite amount of fractions between 0, and 1 (i.e. 1/2, 1/3, 1/4.... 1/1,000,000, etc. etc.) and there are an infinite amount of fractions between 1, and 2, does that not THEORETICALLY mean that 2 is = to 1, and therefore, 1 + 1, which = 2, which is = to 1, is therefore stating that 1 + 1 = 1?

Now, of course I know that's crap (I think) but I'm sure there's actually some sort of theory which proves that concretely....
Mathematical Theory was never my strong point. So.... who knows for sure WHY 1+1 DOES, in fact, = 2.

Well firstly to deal with infinites you need cardinality theory but that is a university maths course so I'm not going to deal with it.
Why does 1+1=2? Because it's an axiom. It's well established that it bears no relation to any object or properties but it's an axiom so it doesn't need to be. If we could prove it it wouldn't be an axiom. It's as simple as that.

Also: Quantum Theorists discovered today that 1+1=3 but only for really high values of 1.
BHS: Bringing you nerd Jokes since 1985.

It was proven by Russell around the turn of the century (I'm too lazy to look it up) that 1+1 = 2. The axioms and notation he used to prove it would be incomprehensible to most of us.

He then found a flaw in mathematical set axioms that allows you to make the set of all sets which do not contain themselves. That set itself is paradoxical, so blah.

Please pass the bong this way when you are done with it.

Not necessarily. The normal axioms used include the equivalents of 1+1=2.
Russel, if I remember correctely, was working on Grand Unified Mathematics but the axioms he used are not in general parlance.
Generally it comes under ther general axioms of m+n=0 and m+k=k+m. All this, of course, relies upon the values set for 1 and 2 which are axiomatic.
As for set theory, its ridiculous (especialy Goedel). Group theory is for champions.

You know I think high level mathematics is like modern-art and economics. You guys actually have no idea what you're saying, you're just trying to trick everyone else into going along with it. 1+1=2 and always will. Well except in binary.

So, yeah. This might just be crazy talk here, but...

How in the hell does that figure?

If you have one dollar (1) and you get another dollar (+1), then you will have two. (=2)

1+1=2

How is that not provable?
Ignore me if I'm being extremely stupid, not in the best mental state right now...

Because there is a limit on the infinities. The summation of the fractions between 1 and 2 must always be less than one, providing a finite restriction on the infinite. Therefore, 2 does not equal 1.

Somebody used the same argument once to prove we never moved. There's an infinite measurement of distance between you and your target, and how can we transverse infinity? But not only is there a limit on the distance that the infinite measurement can go up to, we also have infinite time to transverse that distance.

However, here's another mathematical thought for you. 1/9 is 0.11111111111..., 2/9 is 0.22222222..., 8/9 is 0.8888888888..., but 9/9 is 1!!! So what is 0.99999999....?

It always kind of amused me.

The fractions in between 2 and 1 (1.1, 1.01, etc.) are larger than the fractions between 1 and 0 (.99, .999, etc.), so even though there's an infinite amount of both, the sums of the two ranges do not equal each other, therefore 2 does NOT equal 1.

Darn, you beat me to it.

Man I hate math even more than nature.