Wait what? (1+2+3+4+...

**BAndrew** · 01-14-2014, 07:17 PM

(01-14-2014, 06:41 PM)Naked? No Wrote: But how do you calculate something undefined without simplifying or lose information?

With calculus (that is limits,integrals,derivatives and that sort of stuff)

**eliasfrost** · 01-14-2014, 08:15 PM

I guess I have to remain skeptical because I have no clue how it all ties together. For me infinity means just that, it never ends and it can't be measured but somehow it can be used to produce a result that is finite, it doesn't make any sense. How exactly does it work? Is it all assumptions and theories?

After all, math is an inventions, no invention is perfect.

**BAndrew** · 01-14-2014, 10:13 PM

(01-14-2014, 08:15 PM)Naked? No Wrote: I guess I have to remain skeptical because I have no clue how it all ties together. For me infinity means just that, it never ends and it can't be measured but somehow it can be used to produce a result that is finite, it doesn't make any sense. How exactly does it work? Is it all assumptions and theories?

After all, math is an inventions, no invention is perfect.

How it can produce a result that is finite? Simple:

[Image: 2ccv0ie.jpg]

Underlined: Wrong!!! Mathematics is not an invention. We discover theorems. We don't invent them and we don't create them.

@Bridge

Why is not the following proof valid to you?

We assume that 1 =/= 0,999... =>
(devide by 3) 1/3 =/= 0,333... absurd

Therefore 1=0,999...

How do you explain this?

**eliasfrost** · 01-14-2014, 10:21 PM

But why is it ok to put a limit on something that has no limit?

I don't believe that math is actually natural, I think it's a human invention to understand our surroundings, nothing more nothing less.

**BAndrew** · 01-14-2014, 10:27 PM

(01-14-2014, 10:21 PM)Naked? No Wrote: But why is it ok to put a limit on something that has no limit?

I don't believe that math is actually natural, I think it's a human invention to understand our surroundings, nothing more nothing less.

You don't "put on limit on something that doesn't have a limit". I think you don't understand what the limit really is. What I wrote (as I have said before) reads:
"the limit of 1/x as x approaches +infinity equals 0"

If math is not natural then are you suggesting that (for example) the pythagorean theorem wasn't true before we discovered it? If that is the case then why you can't create any theorem you want?

**eliasfrost** · 01-14-2014, 10:31 PM

But how can something approach infinity, infinity is not a number it's a concept. Can you please explain from the very grounds up how exactly infinity can be used to calculate something, how is it defined (because it has to be in order to be used, otherwise it's just hocus pocus and make-believe) and how can you be so sure that the result is in fact true when a part of the calculation is undefined, that is, have no value?

No, not that it wasn't true before we "discovered" it, but that we didn't know it was applicable before we invented it.

**BAndrew** · 01-14-2014, 10:44 PM

(01-14-2014, 10:31 PM)Naked? No Wrote: But how can something approach infinity, infinity is not a number it's a concept. Can you please explain from the very grounds up how exactly infinity can be used to calculate something, how is it defined (because it has to be in order to be used, otherwise it's just hocus pocus and make-believe) and how can you be so sure that the result is in fact true when a part of the calculation is undefined, that is, have no value?

What do you mean "how can something approach infinity"? Is there something that stops it from doing that? Infinity is an abstract concept describing something without any limit. What you are obviously confusing here is the limit of a function f with unboundedness of infinity. They are two completely different things. If the result wasn't true then how come there are areas (surfaces)? Surfaces consist of infinite points (size 0) and yet they have a certain area. Infinity is not a number, but a concept as you said, but I don't get your reasoning here. I don't treat it like a normal number, I just use it on a calculation.

Quote:No, no that it wasn't true before we "discovered" it, but that we didn't know it was applicable before we invented it.

Then if the theorem was true before we discovered it, it means that it was discovered and not invented.
Listen I don't know what's on your mind, but we don't invent everything.

We invent machines, computers, books, buildings, medicine, maps, tools, clothes, etc.

We don't invent theorems,electrons,particles,mathematical ideas,laws of physics and the universe. We discover them.

**eliasfrost** · 01-14-2014, 10:57 PM

This is going nowhere, I still don't understand how it can be used in a calculation without modifying it's definition or simplifying it. It doesn't make sense to me and probably never will until it's profoundly explained to me.

I never said we invent everything.
But I do believe that math is an invention to understand our surroundings just like we invented language to understand each other. That's what I think, there are no evidence one way or the other so.

**BAndrew** · 01-14-2014, 11:09 PM

(01-14-2014, 10:57 PM)Naked? No Wrote: This is going nowhere, I still don't understand how it can be used in a calculation without modifying it's definition or simplifying it. It doesn't make sense to me and probably never will until it's profoundly explained to me.

I never said we invent everything.
But I do believe that math is an invention to understand our surroundings just like we invented language to understand each other. That's what I think, there are no evidence one way or the other so.

I can't understand what you can't understand.
Derivative is a concept and it is used in calculations
Integral is a concept and it is used in calculations
Function is a concept and it is used in calculations
Sequence is a concept and it is used in calculations
Infinity is a concept so why it can't be used in a calculation? Is there a magic field that says "Oh hello there infinity I am not letting you to participate in this calculation"? If you want to know exactly how this is done then I think you need to learn the corresponding material. Pick a book and start reading.

Math theorems and everything related to it were true before humans where even created. Mathematics existed before humans. Therefore it was not invented by humans, it was discovered by them.

Anyway. I think we are completely off topic right now.

What happens with 1+2+3+4+... ?

**Froge** · 01-14-2014, 11:17 PM

I have a pizza and I want to divide it amongst 2 people. Each person gets half a pizza, i.e. 1 / 2 = 0.5
I have a pizza and I want to divide it amongst 4 people. Each person gets 0.25 of a pizza.
I have a pizza and I want to divide it amongst 100 people. Each person gets 0.01 of a pizza.
I have a pizza and I want to divide it amongst 1 trillion people. Each person gets 0.000 000 000 001 of a pizza.

I have a pizza and I want to divide it amongst a certain number of people, and this number is such that no matter what number you give me, this number is always bigger. How much of the pizza does each person get?