Veeky Forums, when the boys aren't around, what do you think is the most aesthetic number, and why is it e?

and '1' is a symbol, not a number

1 is easily quantified, by something as simple as a stroke: | . The number which "e" claims to stand for can not be represented in any finite fashion.

Totally agree.

Literally a useless number.

except you just "represented" it by assigning it the letter "e". also surely you would agree that the symbol | is not actually the same thing as the number represented by the symbol '1'.

>using strokes for numbers
fucking pussy
real men use dots

"1" or any natural number has basis in reality. A singular stroke is the most primitive example of what we define as "one". For matters of arithmetic, mathematical convention can naturally abstract this to the symbol "1" with its meaning preserved. "e" has no such basis in physical reality. You can't show me "e" things, or something of length "e". I can't even type the number here because of its infinite.

>except you just "represented" it by assigning it the letter "e".

Not an argument. I'm communicating with you using the standard accepted convention. I don't have to agree with it but I use it for argumentation sake.

0

What is the point of using the limit notation when you could just write infinity in place of n?

the point is that the limit at a is not the same as the value of the function at a, even if you compactify R adding infinity as an element

Wrong, a singular stroke can be used to represent one. It is not one itself. Numbers and other mathematical concepts can be used to represent things in reality, or not. Concepts only exist representationally, not as objects in reality.

>e cannot be represented in a finite fashion
>it can be properly defined in ZFC by using for example the pic in OP
you're retarded

I agree that "1" has a basis in reality, but I disagree that it has a physical manifestation independent of human thought. Sure you can point to "one apple", or "one stroke", but there is nothing in physical reality that can serve as an adequate exemplar of the concept of 1 in the Platonic sense. The example of the stroke is misleading due to the simplicity of the physical artifact in question. The usefulness of the concept of 1 is due mainly to its being abstracted from any particular physical object, so to insist that the number is defined through its association to any particular physical representative, simple as it may be, is to defeat the purpose of the abstraction.

At any rate, whether or not any given number has a "basis" in reality is a red herring. 1 and e both have equally sound logical bases in the commonly-accepted axiomatic framework of ZFC. The symbols '1' and 'e' are used by convention to denote these two formal constructs. That is what I meant by "representation". As soon as you can communicate a concept to another person through the use of a mutually agreed-upon signifier attached to that concept (such as the letter 'e'), then you have 'represented' that concept. It makes you difference whether you did it ironically or just for "argumentation sake".

(You)

Dumbass here.

Okay, so with limits, having 1 over infinity makes a zero. Then in that equation, you get 1 to the power of infinity.

Why would that equate to e? 1 to the power of anything is still 1.

you can't just "plug in infinity" whatever you think that means.

Because that number can only go up as n increases.

n is never infinity it just approaches it

Shouldn't it be base 1 then?

no

>lim ∞
/x/ is the other way kid