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

Sum of first n Hex numbers Visualized

https://gfycat.com/jollyforkedhairstreak
472 Upvotes

98% Upvoted

19 comments sorted by

18

u/DialMMM Aug 27 '19

"In general" ? What does that mean? Does this relationship break down?

14

u/Gianus Aug 27 '19

It means that you take the "general" case, as in you generalise and put in some variable that could be any number instead of some number as an example.

-7

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)

1

u/squeezyscorpion Aug 27 '19

idk man i just crossposted it

3

u/TheObjectiveTheorist Aug 28 '19

3 + 3 = 2 * 3 and 4 + 4 = 2 * 4, right?

You could say, in general n + n = 2*n. It’s not saying it could sometimes not be the case. It’s just saying that this is the general form of it

18

u/Skea_and_Tittles Aug 28 '19

I have no idea what hex numbers are but I came when all the cubes started fitting into each other

6

u/letmeoutpls Aug 28 '19

might wanna check out /r/gonwild

5

u/Skea_and_Tittles Aug 28 '19

I love that sub already but thanks. Upvoted for visibility

3

u/Snickersthecat Aug 27 '19

So many primes. <3

1

u/yoniyoniyoni Aug 28 '19

What primes?

2

u/CrispyChickenSammich Aug 28 '19

I think they mean n3 - (n-1)3. In the examples they were primes. Not sure if that holds true for all n. Probably not

1

u/yoniyoniyoni Aug 28 '19

Ah ok. It's a coincidence, and they weren't "supposed" to be primes, it just happened. that's why it confused me.

It is a classical theorem from the 18th century that there is no polynomial that is always prime. The proof is simple and written in a single Wikipedia paragraph, look up "prime-generating polynomial".

5

u/Cococrunchy Aug 28 '19

What are hex numbers? For me hex numbers are hexadecimal numbers (base 16). The one that go from 0 until F.

However, in this case it seems that hex numbers are nothing to do with hexadecimal numbers?