/sci/ - Science & Math

>>8822501
Even in calculus,
[math] \sum_{n=1}^\infty \dfrac{1}{n^2} = \dfrac{\pi}{6} [/math]
You sum rationals and get a non-rational number.

This is not to say that [math] \lim_{m\to\infty}\sum_{n=1}^m n [/math] has a limit in analysis.
It doesn't have a limit in analysis and literally nobody disagrees.

The sum of integers giving -1/12 is one in an entirely different theory (again, everybody agrees) and it has (as physicists know) applications in quantum electrodynamics.
So it's something that has physical applications, just like pic related is a physical application of
[math] \sum_{n=1}^\infty \dfrac{1}{2^n} = 1 [/math],
which is provable in analysis.

Fact of the matter is: You subscribed to mathematical Platonism, a centuries old philosophy that makes you uneasy with interesting and relevant math. Sort yourself out.

>>8822501
Even in calculus,
[math] \sum_{n=1}^\infty \dfrac{1}{n^2} = \dfrac{\pi}{6} [/math]
You sum rationals and get a non-rational number.

This is not to say that [math] \lim_{m\to\infty}\sum_{n=1}^m n [/math] has a limit in analysis.
It doesn't have a limit in analysis and literally nobody disagrees.

The sum of integers giving -1/12 is one in an entirely different theory (again, everybody agrees) and it has (as physicists know) applications in quantum electrodynamics.
So it's something that has physical applications, just like pic related is a physical application of
[math] \sum_{n=2}^\infty \dfrac{1}{2^n} = 1 [/math],
which is provable in analysis.

Fact of the matter is: You subscribed to mathematical Platonism, a centuries old philosophy that makes you crappie with interesting and relevant math. Sort yourself out.