/sci/ - Science & Math » Thread #14107342

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Anonymous Sat 15 Jan 20:29:37 2022 No.14107342 View Reply Original Report

Quoted By: >>14107492 >>14107516 >>14107626 >>14107750 >>14107826 >>14107975 >>14108436 >>14108915

>there are infinitely many numbers between 3 and 4
>none of them are 3 or 4
>one of them is pi
>pi is infinitely long
Mathematically speaking, what the hell is going on with numbers and what does this mean?

Anonymous

Anonymous Sat 15 Jan 2022 21:13:01 No.14107492 Report

Quoted By:

>>14107342
1 has infinitely many 0s after the decimal point
there is no meaning to be gained from this

Anonymous

Anonymous Sat 15 Jan 2022 21:20:45 No.14107516 Report

Quoted By:

>>14107342
because math is infinitely recursive. not only are there infinite numbers between 3 and 4, there are infinite numbers between 3.1 and 3.2, etc. limits are not adequate descriptions of reality, just effective descriptions. reality is infinite

Anonymous

Anonymous Sat 15 Jan 2022 21:51:16 No.14107626 Report

Quoted By:

>>14107342
It’s infinitely “long” but it can be written as a sequence that has a distinct pattern that merely gets more and more specific. Probably not mathematical but I like to think of it as the points between rationals must be infinitely precise. Rationals are infinitely precise as well but they are more “even” (commensurable). Incommensurability is also a good way to think about irrational numbers as well and the original way

Anonymous

Anonymous Sat 15 Jan 2022 22:15:59 No.14107750 Report

Quoted By: >>14107768 >>14107812 >>14108910

>>14107342
3 < ?
3.1 < ?
3.14 < ?
3.141 < ?
3.1415 < ?
3.14159 < ?
3.141592 < ?
3.1415926 < ?
3.14159265 < ?
this continues endlessly
? < ?

Anonymous

Anonymous Sat 15 Jan 2022 22:19:48 No.14107768 Report

Quoted By:

>>14107750
No you can never type all of ? in decimal because it's irrational.

No matter how many digits of ? you type, it will always be a little smaller than ? itself.

Anonymous

Anonymous Sat 15 Jan 2022 22:28:20 No.14107812 Report

Quoted By: >>14107971

>>14107750

If $\langle {a_n}\rangle$ is a convergent sequence with $a_n < a$ then $\lim a_n \le a$ . (eg. you get equality if you take $a_n = 1 - \tfrac 1 n$ and $a = 1$ )

This is another equality case, you have $a_n < \pi$ for each $n$ but $\lim a_n = \pi$ .

Anonymous

Anonymous Sat 15 Jan 2022 22:31:29 No.14107826 Report

Quoted By:

>>14107342
>one of them is thrembo

Anonymous

Anonymous Sat 15 Jan 2022 23:12:45 No.14107971 Report

Quoted By:

>>14107812
this is bozo math

Anonymous

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Anonymous Sat 15 Jan 2022 23:14:45 No.14107975 Report

Quoted By:

>>14107342
you're a homosexual pedophile and you masturbate to children's cartoons

Anonymous

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Anonymous Sun 16 Jan 2022 01:59:12 No.14108436 Report

Quoted By:

>>14107342
Take or self-teach an abstract algebra course. At the field theory section you'll see that there is a logically consistent way to construct the reals (it's a bit of an advanced exercise). The Fundamental Theorem of Algebra then, after R is constructed, is just showing that everything in R splits over C.

Anonymous

Anonymous Sun 16 Jan 2022 04:57:13 No.14108910 Report

Quoted By:

>>14107750
0.9 < 1
0.99 < 1
0.999 < 1
0.9999 < 1
0.99999 < 1

Anonymous

Anonymous Sun 16 Jan 2022 04:59:24 No.14108915 Report

Quoted By:

>>14107342
mfs will claim there's a well-ordering of the reals but can't even point to the smallest number strictly greater than 3

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