It takes over 25 thousand steps to prove that 2+2=4

Originally Posted by Trico

Why take it, then?

Anyway, that is the longest proof that 2+2=4; I don't know how long the shortest proof is, but I imagine it's quite manageable.

Aren't the first few hundred pages of the Principia Mathematica dedicated to proving that 1+1=2?

Proving it from basics is...not easy.

Originally Posted by Sailboat

Why can't you just count on your fingers or something.

Because how do you know that one finger plus one more finger is two fingers? Why isn't it three? Or twelve? Or none?


Of course, my (exceptionally limited) understanding of this is that, despite such proofs, other proofs have popped up showing that it is impossible to prove something as basic as 1+1=2, but I could be mistaken on this point.

Originally Posted by John

Aren't the first few hundred pages of the Principia Mathematica dedicated to proving that 1+1=2?

Proving it from basics is...not easy.


Because how do you know that one finger plus one more finger is two fingers? Why isn't it three? Or twelve? Or none?


Of course, my (exceptionally limited) understanding of this is that, despite such proofs, other proofs have popped up showing that it is impossible to prove something as basic as 1+1=2, but I could be mistaken on this point.

Then wouldn't (logically) a significant number of the steps be devoted to proving that the numbers 1, 2, 3 and 4 exist in the first place? And that numbers can be added together?



It's all rather silly anyway; numbers mean whatever we want them to mean.

Well, **** it.

I'm done with this math crap for good.

Originally Posted by Rew

That is only appropriate, really. :3

Thats is just awesome.

How do people have the time and patience to actually sit down and prove all this nonsense and write out a hundred pages of it explaining it to us lesser beings?

Originally Posted by Eggys

How do people have the time and patience to actually sit down and prove all this nonsense and write out a hundred pages of it explaining it to us lesser beings?

Because they know they'll get paid to do it.

Originally Posted by Devout Justice

*Sigh* And I thought Calculus was hard lol!

Calculus is not hard. The calculus may be.
Sorry had to. I found calculus um fun. It was just time consuming. It took a lot of work to get concepts down to a science. but there was nothing that was like a wall I couldn't get past. Oh and I found that really cool. All be it very nerdy.

Originally Posted by Sabbo

It's all rather silly anyway; numbers mean whatever we want them to mean.

Exactly. They are nothing more than variables (in a C++ sense). We are told from birth what value each number holds. More or less. 1 is the name we give to a lone item. I feel that one could argue that 1 has no value, until it is given to an item. That kinda goes without saying, to me at least. This is the kinda stuff I waste half my day thinking of. To tell the truth.

Originally Posted by John

Aren't the first few hundred pages of the Principia Mathematica dedicated to proving that 1+1=2?

Proving it from basics is...not easy.


Because how do you know that one finger plus one more finger is two fingers? Why isn't it three? Or twelve? Or none?


Of course, my (exceptionally limited) understanding of this is that, despite such proofs, other proofs have popped up showing that it is impossible to prove something as basic as 1+1=2, but I could be mistaken on this point.

I would take the line that simple truths, like that 1+1=2, should simply be apprehended by the intellect, much like the principle of non contradiction.

Of course, my field is religion, not philosophy, and the extent to which I have a solid understanding of philosophy only really reaches the medievals. I can't help but approach this problem with Neoplatonism in mind, which is not how any legitimate math people go about their business.

I didn't understand a single word on that page.

More or less. 1 is the name we give to a lone item. I feel that one could argue that 1 has no value, until it is given to an item. That kinda goes without saying, to me at least.

The ability to count (in general) evidences not only that you hold an abstract concept of a non-physical "number one", but also that such a concept has important applications. That you recognize an inherent similarity between a lone apple and a lone orange, or between a pair of grapes and a pair of berries should prove to you that you have mental concepts "one-ness" and "two-ness" that extend beyond your empirical familiarity with fruit.

People dismiss the relevance/existence of the natural numbers too often, I think, because the abstraction falls close enough to the pure experience as to blur the distinction... but did you know that when we employ the natural numbers to describe all the ways in which "a" elements may be chosen from a set of "b" possibles (an important question in probability) we employ an abstraction identical to that used to determine which polygons of odd-numbered sides can be constructed with a compass and straight-edge (an important question in geometry)? If that natural numbers were really inseperable from the physical world, that would be utter nonsense!

I can't help but approach this problem with Neoplatonism in mind, which is not how any legitimate math people go about their business.

Well... its how the (arguably) most important name in this particular field of Maths (Russell) went about /his/ business, so I might have to disagree

Originally Posted by KillerKat55

Calculus is not hard. The calculus may be.
Sorry had to. I found calculus um fun. It was just time consuming. It took a lot of work to get concepts down to a science. but there was nothing that was like a wall I couldn't get past. Oh and I found that really cool. All be it very nerdy.

Oh boy, Calculus was my favorite class as a senior. <3 Even though the teacher kind of...erm...sucked, I still loved going back to that class to see what crazy things we would learn next. My proudest moment was when I solved a problem not even the teacher could figure out. Boy did I feel nerdy.

But...I can't wait to go back to college and see an algebra/trig/calculus problem again. It will be a great feeling, coupled with frustration because I haven't taken any math classes for a year. ;p

I've spent hours trying to get the details of those steps to see that logic :'D

Hey look!
First I have 2: ||
Then I add another 2: ||
Now look how many I have!! ||||

Four!
And I think that's less than 25,000 steps, I lost count.

I wonder how many steps it take to tell folks you can't prove or disprove that God exist.

Originally Posted by Snow_Storm

I wonder how many steps it take to tell folks you can't prove or disprove that God exist.

Only God knows.

Originally Posted by Link the Mini

Only God knows.

Hah. XD

But yeah. This math thing... seriously makes me feel like an idiot. I took a look at a couple links to see if I could even begin to comprehend any of the content.... yeah, no. PHAIL. Excuse me while I wipe the drool from my awed, gaping mouth.

This is exactly why I hate math...

That is a beautiful proof. It only takes such a long time to solve because no assumptions are made - many hypotheses have to be justified along the way.

There's this small magical device called a calculator. T'is a gift from heaven if you ask me!

Calculator says: Screw logic and listen to me!
I reply: I'm all ears!