The Reimann Hypothesis is an interesting topic to me, but as a high school student, I can’t seem to find an understandable definition of a trivial zero. How could an infinite sum result in nothing?
In: Mathematics
Trivial is the term of art there, zero’s is just the result of the hypothesis in question.
Triviality in mathematics just means roughly what it does every where else; unimportant. From Wolfram: “Related to or being the mathematically most simple case. More generally, the word “trivial” is used to describe any result which requires little or no effort to derive or prove.”
So in the case of, “All non-trivial zeros of the Zeta function have real part one-half.” it’s just letting you know in a formal sort of way to exclude that set of trivial zeros the function spits out.
For a more technical, not ELI5 explanation the second answer here is a good one: https://math.stackexchange.com/questions/138112/what-does-it-really-mean-for-something-to-be-trivial
>The trivial map usually sends either everything to 0 or to 1 or to itself, depending on the context.
>The trivial solutions to xn+yn=zn
are when x=y=z=0, x=z=1 and y=0, or y=z=1 and x=0
>The trivial subgroups of a group are the whole group itself and the one-element subgroup.
>Or it means that the author doesn’t want to spell out something which is (in the author’s view) and easy/obvious fact. I think most commonly, though, it means a student is bluffing on his homework with something he or she can’t quite prove.
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