Is there a scientific reason why you cannot find a one-to-one correspondence between the integers and the rational numbers no matter how hard you try?
Jew lies desu senpai.
>>7808345
Because every integer is also a rational number (except for 0)
>>7808345
You just haven't tried hard enough.
>scientific reason
It's not science. It's mathematics.
The cardinality is different
I know there is one for positive integers and positive rationals
I don't know about negatives, though
Integers are quantized, rationals aren't.
>>7808345
This is one of the things that I've never been able to wrap my head around. I can get the whole finding a number that exists in irrationals but can't in rationals thing, but simply numbering them? This is one case where it hurts my head because no matter how many numbers are between whatever arbitrary numbers you have from the rationals, you'll still have enough integers to cover those because the integers don't end. I get how each time you iterate to the next rational number, the integers get further and further behind; however, the integers will eventually get to that point...
To me, saying you can't create a one to one for this is like saying that just because a car is travelling at 10mph, it can't pass the same 100 miles that the car going 1000mph was going.
>>7808345
its simple
Z->N->Q
done.
>>7808435
wut?
>>7808345
isn't this false? The cardinality of N and Q is the same isn't it?
but you can lmao
>>7808385
Why isn't zero a rational? It can be expressed as the quotient of two integers.
>>7808510
0/0 is undefined, it does not equal zero.
>>7808518
0/1 you dumb fucking fuck
