/sci/ - Science & Math

[Anonymous No.5306356]

So I was sitting in class today, bored, and I thought of a math problem. I'm not sure if it's been thought of before (though it probably has) and I was wondering if anyone has any info on it.

In my head, it started off as A and B are any numbers, say long, weird decimals, and M and N are integers. I was wondering if, for any A and B values, there exists an M and N where MA = NB. This evolved in my head to M/N=B/A, and so (I think) the final question is: Can every number be expressed as a ratio of 2 integers?

Sorry if this is stupid or obvious, or if I'm missing something

[Anonymous No.5306362]

http://en.wikipedia.org/wiki/Irrational_number

[Anonymous No.5306368]

>>5306362
Ah, thank you.

Now I feel like I should have thought of this earlier, oh well. I appreciate it.

[Anonymous No.5306372]

If a,b are any numbers and r,s are members of the rationals, then actually any relation ar + bs = 0 is called an algebraic dependence relation. More generally, if f(x,y) is a polynomial over the rationals, then if f(a,b) = 0 then a,b are called algebraically dependent. This can be extended to any number of elements. And yes, there indeed do exist sets of algebraically independent (over the rationals) real numbers.

[Anonymous No.5306376]

>>5306368
You're welcome.

It's a pretty solid question to ask yourself.

[Deaner's Left Nut !S0ooHAHDTU No.5306377]

No, nobody has ever wondered if every number can be expressed as the ratio between two integers. EVER. You are certainly the first. You are a very special butterfly.

[Anonymous No.5306382]

>>5306377
0/10

[Deaner's Left Nut !S0ooHAHDTU No.5306385]

>>5306382

autism/1000

[Anonymous No.5306393]

>>5306385
Autism isn't even a number.