/sci/ - Science & Math

[Anonymous No.10400014]

How can people believe in infinitesimals if they would be written as 0.(0)1 if 9.(9) = 10

[Anonymous No.10400109]

Belief has little to do with it, other than the belief that it just werks.
A bit like a Laplace transform, you fiddle around in a s-variable wonderland, and in the end you come back to x or t.

[Anonymous No.10400292]

>>10400014
https://www.youtube.com/watch?v=BBp0bEczCNg

https://www.youtube.com/watch?v=FVZqPaH94qU

[Anonymous No.10400533]

consider it a concept rather than a number

[Anonymous No.10400663]

>>10400533
A number is a concept.

[Anonymous No.10400688]

>>10400663
Numbers are just an abstract conception of geometric reality.

[Anonymous No.10400693]

>>10400688
>Numbers are an abstract conception of the geometric reality
No ,numbers are real

[Anonymous No.10400712]

>>10400014
Nobody "believes" in infinitesimals except for wackjob non-standard analysts and physicists/engineers/students who were never taught any better.

[Anonymous No.10400919]

>>10400109
1/-12 is BELIEVED to be the sum of all integers, but it doesn't converge so I can say -1/8 = Sum of all integers

Proof: 1 + 2 + 3 + 4 + 5 + 6 + 7+... = S
1 + (2+3+4) + (5+6+7)+...=S
1 + 9 + 18 + 27 +... =S
1+9(1+2+3+4+5+...)=S
1+9S=S
1=-8S
S=-1/8
So yes I can say it and I don't care just because a lot of people say it's one way doesn't mean it is think for yourself

[Anonymous No.10400927]

>>10400014
infinitesimals are placeholders to talk about the idea of convergence of a limit

[Anonymous No.10400945]

>>10400919
1/-12 is not believed to be the sum of all integers you actual fucking mong.
It's some stupid popsci trick where the instead of calculating an infinite series of 1-1+1-1+1-1+1 you just say it equals one half, which is obviously not true.

All those other smart tricks are just extensions of the riemann function into domains it does not apply to, and then extrapolating those results to get finite calculations in the domain it originally worked on.
It's bogus.

[Anonymous No.10400948]

>>10400945
>It's some stupid popsci trick where the instead of calculating an infinite series of 1-1+1-1+1-1+1 you just say it equals one half, which is obviously not true.
1-1+1-1+1-1... = x
x = 1 - x
2x = 1
x = 1/2

[Anonymous No.10400955]

>>10400945
>>10400948
z = 1+i-1-i...
z = 1+iz
z-iz = 1
z(1-i) = 1
z = 1/(1-i)

[Anonymous No.10401003]

>>10400945
>>10400948
>>10400955
In fact, generally
[math]
z(x) = \sum^{\infty}_{n=0}e^{2*pi*i*n \over x}
= 1 + e^{2*pi*i \over x} * {\sum^{\infty}_{n=0}e^{2*pi*i*n \over x}}
= 1 + e^{2*pi*i \over x}*z(x)
z(x)-e^{2*pi*i \over x}*z(x)=1
z(x)(1-e^{2*pi*i \over x})=1
z(x)={1 \over 1-e^{2*pi*i \over x}}
[/math]

[Anonymous No.10401027]

>>10400955
>>10401003
[math]
\begin{align}z(x) &= \sum^{\infty}_{n=0}e^{2\pi in \over x}\\
&= 1 + e^{2\pi i \over x} {\sum^{\infty}_{n=0}e^{2\pi in \over x}}\\
&= 1 + e^{2\pi i \over x}z(x)\\\end{align}
[/math]
Thus
[math]
z(x)-e^{2\pi i \over x}z(x)&=1\\
z(x)(1-e^{2\pi i \over x})&=1\\
z(x)&={1 \over 1-e^{2\pi i \over x}}\end{align}
[/math]