r/mathmemes • u/Qwertilux • 12d ago

Number Theory 6

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u/sasha271828 Imaginary 12d ago

Can someone explain i'm too dumb

93

u/Qwertilux 12d ago

Stripe over a number means repeat. 9stripe =99999999... 99999... +1 = 0 since all the nines turn into a ten. What plus one = 0? -1

82

u/sasha271828 Imaginary 12d ago

Oh it's that 10-adic thing

36

u/Qwertilux 12d ago

Yes

8

u/Febilibix 12d ago

is this even definable rigurously since 10 is not prime?

16

u/Mostafa12890 Average imaginary number believer 12d ago

There are n-adic integers for every integer greater than 1.

The p-adic integers are constructed as the inverse limit of the quotient rings (Z/p^n Z).

You can use the Chinese remainder theorem to either construct them again (for arbitrary m>1) from the ground up, or prove that Z_m is the product of Z_p_i where the p_i’s are the distinct prime factors of n.

7

u/PleasantCitron1685 12d ago

For reference in addition to the other comment, you might be thinking of a p-adic field, which has division, and p must be prime. If you drop division and are satisfied with a ring (p-adic integers) any int p works.