/sci/ - Science & Math » Thread #11357215

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Anonymous Mon 03 Feb 16:50:03 2020 No.11357215 View Reply Original Report

Quoted By: >>11357239

>formal derivative of the formal sum of two formal power series
Do mathematicians really just stick "formal" in front of words to ignore all the rules for dealing with them?

Anonymous

Anonymous Mon 03 Feb 2020 16:55:13 No.11357226 Report

Quoted By: >>11357230

Actually, it's called formal because it's a purely algebraic construction.
You can just prove linearity and the product rule from the expression given, but it's really not worth the effort.

Anonymous

Anonymous Mon 03 Feb 2020 16:57:55 No.11357230 Report

Quoted By: >>11357376 >>11357423

>>11357226
But when you put "formal" in front of a power series suddenly you stop caring about convergence
Seems like a get out of jail free card

Anonymous

Anonymous Mon 03 Feb 2020 17:03:59 No.11357239 Report

Quoted By:

>>11357215
this is algebraic foppery not math

Anonymous

Anonymous Mon 03 Feb 2020 18:10:39 No.11357376 Report

Quoted By:

>>11357230
Algebra is basically giving names to things with certain properties you like and then doing various things with them prove or disprove stuff.

Anonymous

Anonymous Mon 03 Feb 2020 18:13:45 No.11357382 Report

Quoted By:

the power of universal constructions (and some of its more general cases)

Anonymous

Anonymous Mon 03 Feb 2020 18:32:47 No.11357423 Report

Quoted By:

>>11357230
You stop caring about convergence because convergence doesn't even make any sense. A formal power series is not a function. It's a sequence of numbers.

The fact that you are concerned that it might not "converge" means that you are still stuck in the idea that these things are supposed to be functions.

Anonymous

Anonymous Mon 03 Feb 2020 18:55:47 No.11357456 Report

Quoted By:

>power series

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