/sci/ - Science & Math

[Anonymous No.9726759]

Consider Z as subset of R in the canonical way. We're gonna construct a subset S between the two by iterating a function, namely

[math] h(x,y) := (x+y) / 2 [/math]

So since e.g. 2 and 3 are in S, the value 5/2 or 2.5 is in S too. And since 5/2 and 7 is in S, the value 19/2 or 4.75 is too.

Does S end up being Q?

If not, is there another function h' which does the job?

[Anonymous No.9726764]

(I meant 19/4, not 19/2)

[Anonymous No.9726774]

>>9726759

you'll probably end up with a subring of Q

[Anonymous No.9726781]

Tell me how you'd get 1/3.
Think for yourself for once you fucking idiot.

[Anonymous No.9726854]

>>9726759
>Does S end up being Q?
No u fukin retard
how can you get [math]\frac{1}{3}[/math] by dividing integers by two repetitively

[Anonymous No.9726930]

>>9726774
That comment raises the question which structures are permissible on that set.

Has the set anything to do with some p-adics?

If it's a ring, is it iso to e.g. Z?

[Anonymous No.9726953]

>>9726759
of course not, every element of S is of the form
[math]\frac{p}{2^q}[/math]
where p and q are integers.
if you want S to contain more elements, then you will need some other axiom, like the completion axiom, or any axiom where an infinite set of numbers can represent a number

[Anonymous No.9727214]

>>9726759
I dont believe in the Reals sorry

[Anonymous No.9727233]

>>9726759
>kat.jpg
bent u een nederlander? :)

[Anonymous No.9727252]

>>9727233
German. Katze.

[Anonymous No.9727255]

>>9726953
well S, and any subring of Q with elements m/p^n with p a fixed prime, will be dense in R anyway

[Anonymous No.9727268]

>>9727252
So you saved a dutch cat or why the filename?

[Anonymous No.9728783]

>>9726774
Q doesn't have any nontrivial subrings