Comment by gunnihinn
1 month ago
A distribution is not a function. It is a continuous linear functional on a space of functions.
Functions define distributions, but not all distributions are defined that way, like the Dirac delta or integration over a subset.
A functional is a function.
The term "function" sadly means different things in different contexts. I feel like this whole thread is evidence of a need for reform in maths education from calculus up. I wouldn't be surprised if you understood all of this, but I'm worried about students encountering this for the first time.
Don’t know if you are a mathematician or not but mathematically speaking “function” has a definition that is valid in all mathematical contexts. Functional clearly meets the criteria to be a function since being a function is part of the definition of being a functional.
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