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

[eliasfrost]

You can't calculate infinity, but it is used in calculations

But how can you use something unmeasurable to perform a calculation? I'm not trying to disprove anything I'm just curious.

[Bridge]

How do you calculate with something that is infinite? I'm no math-head but it seems like infinity is something that can't be measured and therefore have no place in a calculation? Or maybe I'm too stupid?

No, that is essentially what I am arguing. It's not a tangible number, and the proof that BAndrew posted uses a concept called limits. In this case it's expressed by "lim(x->y)" - colloquially, it's often read as "x approaches y". The entire crux of the issue is that limits are used to make impossible calculations possible and they give approximate values - and this is being presented as incontrovertible proof that the endless sequence of 0.000… infinitely many decimals … 0001 converges at a certain point and becomes nonexistent, when common sense dictates that it's impossible for something to be so small that it doesn't exist. Infinity and infinitesimal numbers are not real numbers to be used in calculations because they don't have any real representation and therefore are impossible to use in calculations.

You are not providing any proof of your statements.

Because my argument is that there is no proof. I reject the facile proofs on the grounds that it assigns fixed values to unknowable concepts.

But if you feel so strongly about it, prove to me that "the limit of 1/n as n approaches infinity is 0". Without using limits or algebra or anything which is designed for real numbers.

Then perhaps the way you perceive the universe is wrong?

Oh yes, and it almost certainly is. However, I'm not the one making assumptions.

[BAndrew]

@Naked? No
A good example is the integral. For instance with an integral you can calculate the area of a function exactly by calculating the sum of infite infinitesimals I am not going into details into how that works. You can read here, but it requires some more advanced mathematical knowledge.

@Bridge

By rejecting the use of infinitesimals and infinity in calculations you are rejecting a whole branch of mathematics which by the way works just perfectly.

But if you feel so strongly about it, prove to me that "the limit of 1/n as n approaches infinity is 0". Without using limits or algebra or anything which is designed for real numbers.

If I have to prove something I have to start from somewhere (axioms) don't you think? The definition and explanation of a limit is the following (from wikipedia):

Suppose f is a real-valued function and c is a real number. The expression



means that f(x) can be made to be as close to L as desired by making x sufficiently close to c. In that case, the above equation can be read as "the limit of f of x, as x approaches c, is L".

Augustin-Louis Cauchy in 1821,[2] followed by Karl Weierstrass, formalized the definition of the limit of a function as the above definition, which became known as the (ε, δ)-definition of limit in the 19th century. The definition uses ε (the lowercase Greek letter epsilon) to represent a small positive number, so that "f(x) becomes arbitrarily close to L" means that f(x) eventually lies in the interval (L - ε, L + ε), which can also be written using the absolute value sign as |f(x) - L| < ε. The phrase "as x approaches c" then indicates that we refer to values of x whose distance from c is less than some positive number δ (the lower case Greek letter delta)—that is, values of x within either (c - δ, c) or (c, c + δ), which can be expressed with 0 < |x - c| < δ. The first inequality means that the distance between x and c is greater than 0 and that x ≠ c, while the second indicates that x is within distance δ of c.

Note that the above definition of a limit is true even if f© ≠ L. Indeed, the function f need not even be defined at c.

If n-->infinity then we define:

The sequence a(n) has a limit L ∈ ℝ and we write

lim a(n) = L if for every ε>0, exists a n0 ∈ ℕ* such that n>n0 then
n-->∞

|a_n - L| < ε

It is really Math heavy going. If you don't accept the definition of course then I can't prove anything

[eliasfrost]

A good example is the integral. For instance with an integral you can calculate the area of a function exactly by calculating the sum of infite infinitesimals I am not going into details into how that works. You can read here, but it requires some more advanced mathematical knowledge.

I still don't understand how infinity can be used in calculation, if you use something unmeasurable to calculate something, doesn't that also make the result unmeasurable?

[BAndrew]

I still don't understand how infinity can be used in calculation, if you use something unmeasurable to calculate something, doesn't that also make the result unmeasurable?

Not necessarily. For example a string has an infinite ammount of points but a finite length.

[eliasfrost]

How can a finite line have an infinite amount of points?

[BAndrew]

How can a finite line have an infinite amount of points?

Because points are 0 in size.

[eliasfrost]

How can a finite line have an infinite amount of points?

Because points are 0 in size.

Then there are no points.

[BAndrew]

Wait what? There are no points?

[eliasfrost]

If the points have no size, then how are there any points? And how can you be so sure that there even are infinite of them?