Math peeps explain this to me

[Dari]

How? Explain

what does the area on the left side of the parabola with limited range have to do with the series on the right side with a range of infinity?

 

[purbeast0]

i've watched the first 20 seconds of the video and already see a major flaw...

he says "all the numbers 1 + 2 + 3 + ... all the way up to infinity".

the problem is ... there is no such thing as "all the way up to infinity" as infinity is never ending.

don't even know if it's worth while watching the rest of the video with the premise of it being so wrong. he has the basic concept of infinity wrong from the get go.

it is just like how infinity + infinity = infinity.

or infinity * infinity = infinity

all it means is never ending numbers.

EDIT:

lol wow this video is retarded, not watching if after seeing what they say the sum of S1 = .5.

you can't take an average of a never ending sequence of numbers. but they conveniently do just to "prove" their point.

simply retarded.

 

[Attic]

I get that the mathematical hocus pocus is required to get the -1/12.

What are we actually explaining here?, vid would be upgraded if we were told what in physics is coming to this -1/12 number as that appears to be some of the leverage used for why this proof is legit.

Obviously adding the series 1+2.... does not equal nor converge on a limit of -1/12, so we are measuring something else. I'm unclear on what we are actually measuring, what's the physics application for this? and where is the fit needed within that application. Are they designing actual physical objects or lasers with this rule, or is this all theory?

 

[Cerpin Taxt]

i've watched the first 20 seconds of the video and already see a major flaw...

he says "all the numbers 1 + 2 + 3 + ... all the way up to infinity".

the problem is ... there is no such thing as "all the way up to infinity" as infinity is never ending.

His wording is poor, yes. The function is still sound, however. At the same time, it isn't really true to say that "infinity is never ending." Infinity is a constant. It isn't a rolling counter that is currently running and will never stop.

don't even know if it's worth while watching the rest of the video with the premise of it being so wrong. he has the basic concept of infinity wrong from the get go.

it is just like how infinity + infinity = infinity.

or infinity * infinity = infinity

all it means is never ending numbers.

EDIT:

lol wow this video is retarded, not watching if after seeing what they say the sum of S1 = .5.

you can't take an average of a never ending sequence of numbers. but they conveniently do just to "prove" their point.

simply retarded.

The result of 1/2 isn't strictly arrived at by "just taking the average." That's just the simplification he used in the video, while linking to another video that proves that 1/2 is the valid sum.

 

[purbeast0]

His wording is poor, yes. The function is still sound, however. At the same time, it isn't really true to say that "infinity is never ending." Infinity is a constant. It isn't a rolling counter that is currently running and will never stop.

i don't think you grasp what infinity means.

http://www.mathsisfun.com/numbers/infinity.html

it is a concept of a never ending number. it is not a "constant" as you say. it is a concept of a number that is never ending and has no finite end and goes on forever and ever.

just like 1/3 is .333 repeating forever. it repeats infinity times, ie., it never stops repeating.

EDIT:

some of the examples on that page are good, especially this one kind of fits this whole stupid video...

An infinite series of "A"s followed by a "B" would NEVER have a "B".

just like the "infinite series of 1 + 1 - 1 +..." would never "end" so you can never have an average/summation of 1/2.

just like there are "infinite" points in a line. the amount of points in a line never ends because you can be at .1, .01, .001, ...

 

[Chaotic42]

His wording is poor, yes. The function is still sound, however. At the same time, it isn't really true to say that "infinity is never ending." Infinity is a constant. It isn't a rolling counter that is currently running and will never stop.

What system are you working with that you claim infinity is a constant?

 

[Cerpin Taxt]

i don't think you grasp what infinity means.

http://www.mathsisfun.com/numbers/infinity.html

it is a concept of a never ending number.

"Never ending" implies that it a process is underway. But there is no process. A quantity is finite or it is infinite, but it remains a fixed value.

....it is not a "constant" as you say. it is a concept of a number that is never ending and has no finite end and goes on forever and ever.

"Does not have an end" is not the same as "goes on forever and ever." It isn't on-going. It is already infinite. It didn't "arrive" there. It isn't "on the way" to something. It simply is infinite. Constantly.

...just like 1/3 is .333 repeating forever. it repeats infinity times, ie., it never stops repeating.

No. Maybe it you'd prefer that I refer to it as a "value." It isn't really accurate to say that 0.333... repeats "infinity times." There are an infinite number of 3's. They are all there, already. They aren't "still going."

EDIT:

some of the examples on that page are good, especially this one kind of fits this whole stupid video...



just like the "infinite series of 1 + 1 - 1 +..." would never "end" so you can never have an average/summation of 1/2.

The series represented is a whole. It is an ordered set with no greatest element, but it is a set nonetheless.

just like there are "infinite" points in a line. the amount of points in a line never ends because you can be at .1, .01, .001, ...

This is somewhat just a difference in semantics, but you need to understand that infinity is a mathematical object -- specifically a type of set. It isn't a process. It is already whole.

 

[Cerpin Taxt]

What system are you working with that you claim infinity is a constant?

I'm working with math. Seriously. It isn't a variable. It is a constant. Period. It is a peculiar kind of constant, to be sure. It's value is fixed, however.

 

[purbeast0]

you clearly don't grasp the concept of infinity. i'll agree to disagree.

 

[lozina]

<< So glad never pursued a career in 'the maths'

 

[Cerpin Taxt]

you clearly don't grasp the concept of infinity. i'll agree to disagree.

No, really. I do. The things I said were even included in the link you offered.

Infinity does not grow

Infinity is not "getting larger", it is already fully formed.

Sometimes people (including me) say it "goes on and on" which sounds like it is growing somehow. But infinity does not do anything, it just is.

If it isn't growing, then it is constant. It is not finite, it is infinite, constantly.

 

[purbeast0]

No, really. I do. The things I said were even included in the link you offered.



If it isn't growing, then it is constant. It is not finite, it is infinite, constantly.

i never said "its always growing" i said "it is never ending".

you simply cannot take an average of something that is never ending, because the sum of the numbers in the group you want to take an average of, is divided by the size of that group, which has to be a finite number. you can't put a never ending number as the denominator to find an average.

so their idea of finding an average sum of 1/2 of an infinite set simply makes 0 sense.

and no, infinity is NOT a constant. a constant means that the value means the same thing everywhere. if that were the case, then infinity/infinity would equal 1, and it doesn't. it equals infinity, as that link i pasted shows.

if infinity were a constant, then infinity + infinity would equal 2 * infinity, which it doesn't. it equals infinity.

 

[Cerpin Taxt]

i never said "its always growing" i said "it is never ending".

You said it "goes on forever and ever," and "it never stops." These are false statements. Infinite sets are not "never ending." They are complete. They are whole.

you simply cannot take an average of something that is never ending, because the sum of the numbers in the group you want to take an average of, is divided by the size of that group, which has to be a finite number.

Strictly speaking, that isn't what he did. If you click on to the next video where the result of 1/2 is explained, you'd understand it.

...you can't put a never ending number as the denominator to find an average.

Again, infinite numbers are not "never ending."

so their idea of finding an average sum of 1/2 of an infinite set simply makes 0 sense.

Your incredulity does not invalidate the math.

and no, infinity is NOT a constant.

Actually there are infinitely many infinite constants. Take the Aleph numbers, for example.

...a constant means that the value means the same thing everywhere.

The value of Aleph_null is the same everywhere.

...if that were the case, then infinity/infinity would equal 1,

No, that is not the case. That is only true of finite constants.

...and it doesn't. it equals infinity, as that link i pasted shows.

Your ideas seem to be a case of "garbage in, garbage out."

if infinity were a constant, then infinity + infinity would equal 2 * infinity, which it doesn't. it equals infinity.

You're using operations defined on finite numbers, so the mistake is yours, not mine.

Let me ask you this: how could we know that some infinities are larger than others? If they do not have a constant value, then we could not evaluate inequalities, yet mathematicians do it all the time.

 

[purbeast0]

Again, infinite numbers are not "never ending."

you are just flat out wrong.

What is Infinity?


Infinity ...

... it's not big ...

... it's not huge ...

... it's not tremendously large ...

... it's not extremely humongously enormous ...

... it's ...

Endless!

Infinity has no end

Infinity is the idea of something that has no end.

In our world we don't have anything like it. So we imagine traveling on and on, trying hard to get there, but that is not actually infinity.

So don't think like that (it just hurts your brain!). Just think "endless", or "boundless".

If there is no reason something should stop, then it is infinite.

i'm sorry if you can't grasp this concept.

 

[Cerpin Taxt]

you are just flat out wrong.

No, really. I'm not. "It has no end" is just lay-speak for "the set has no greatest element." The set isn't still growing, however. It is whole. It is complete. All of the elements are already there at the same time.

In simpler terms, you took "it has no end" and turned it into "it's never ending." The former is true as I described above, although the lay-speak is somewhat sloppy. The latter implies that it is an on-going process without a fixed value, and it is wrong.

Aleph_null is a cardinal number. It is a constant with a fixed value. It is the number of elements in the set of natural numbers, and it is infinite.

i'm sorry if you can't grasp this concept.

I grasp it quite clearly. I can also see quite clearly that you have misunderstood your own references.

EDIT: I should add that this part of what you quoted is maybe what's misleading you:

If there is no reason something should stop, then it is infinite.

This isn't really true. It implies that if a process went on long enough it would "reach infinity," and that's false.

 

[purbeast0]

so now you are arguing that "endless" and "never ending" and "has no end" all mean different things?

http://dictionary.reference.com/browse/never-ending

never-ending
[nev-er-en-ding] Spell Syllables
Examples
adjective
1.
having or likely to have no end:

yeah i'll agree to disagree with you. you aren't making any sense at all to me. we'll leave it at that

 

[Cerpin Taxt]

so now you are arguing that "endless" and "never ending" and "has no end" all mean different things?

http://dictionary.reference.com/browse/never-ending

No, I'm saying that "never ending" describes a process while "has no end" describes an object. Infinite numbers are mathematical objects. They are not processes. When you speak about infinity as though it were a process, you are speaking wrongly.

Look, I'm trying to help you disabuse yourself of the misconceptions you imparted upon yourself when you decided to base your entire argument on a definition written for lay-people. If you'd prefer to continue holding wrong ideas because you cannot accept the rigors of actual mathematical facts, that's your prerogative.

yeah i'll agree to disagree with you. you aren't making any sense at all to me. we'll leave it at that

Infinity is not a common-sense idea, but it is well-understood. It is easy to have some wrong ideas about infinity if you try to think about it in common-sense ways.

 

[Puppies04]

What is This thread? This thread ... ... it's not big ... ... it's not huge ... ... it's not tremendously large ... ... it's not extremely humongously enormous ... ... it's ... Endless!

Makes perfect sense

 

[disappoint]

No, really. I'm not.

The stubbornness is glorious in this one.

Oh and yes really, you are.

 

[disappoint]

You said it "goes on forever and ever," and "it never stops." These are false statements. Infinite sets are not "never ending." They are complete. They are whole.

Nope. Nope nope nope nope. Infinite sets are never ending.

 

[purbeast0]

don't even bother dude it's not worth it lol.

 

[Cerpin Taxt]

Nope. Nope nope nope nope. Infinite sets are never ending.

Sets are not processes. They are objects. It's that simple.

 

[Chaotic42]

I'm staying out of this, but this is why mathematics has formal definitions for terms.

 

[Cerpin Taxt]

The negative natural numbers are an infinite set that "end" at -1.

Whoops. How'd that happen?

 

[disappoint]

don't even bother dude it's not worth it lol.

Look, I'm trying to help you disabuse yourself of the misconceptions you imparted upon yourself when you decided to base your entire argument on it not being worth it. If you'd prefer to continue holding wrong ideas because you cannot accept the rigors of actual stubborn numbskull bashing, that's your prerogative.