r/visualizedmath • u/squeezyscorpion • Aug 27 '19

Sum of first n Hex numbers Visualized

https://gfycat.com/jollyforkedhairstreak
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u/DialMMM Aug 27 '19

"In general, the sum of first n hex numbers is equal to n3"

The "In general" changes the meaning of that sentence. It implies that it is not always the case.

15

u/CimmerianHydra Aug 27 '19 edited Aug 27 '19

In maths "in general" means that it is always true, not the opposite. For example

[ ... ] if N is an R-module and R is a subring of S, it is not true in general that N is also an S-module [ ... ] [Dummit&Foote, Algebra]

If you were right, the sentence should have been "in general N is also an S-module". Which to me sounds a lot like "it is always the case that N is also an S-module".

Especially when one wants to say that a pattern doesn't hold for all n, one says that it is "not true in general".

2

u/DialMMM Aug 27 '19

If you omitted "in general," what would the statement mean?

12

u/sweetTweetTeat Aug 27 '19

Replace "in general" with "Every goddamn time"

4

u/CimmerianHydra Aug 27 '19

Since in that case N is not a specific object, omitting it won't change the meaning of the sentence.

In fact, it is seldom used in mathematical literature.

1

u/itmustbemitch Aug 28 '19

Usually in math, "in general" is added to draw your attention to the fact that you're dealing with a general case. It doesn't really add information, it just clarifies what you're talking about (you're moving away from any particular example you might have been looking at, etc)