> Almost all
I love this comment because it brings back memories of school.
In a layman's terms, I think almost all in this case means all but a finite amount
can we say almost all real numbers are irrational?
1 1/1 2/1 3/1 4/1 5/1 ... 2 1/2 2/2 3/2 4/2 5/2 ... 3 ...
so clearly we can count all the rational numbers but how many irrational numbers are there? are there (many) more irrational numbers than there are rational numbers?
http://austinrochford.com/posts/2013-12-31-almost-no-rationa...
So all of the irrationals that we use or could ever use in calculations are countable. The uncountability of the irrationals comes entirely from the uncomputable ones, which we will probably never see.
The reals are deeply weird.
Infinity is funny like that.
The conclusion that there are somehow more irrationals than rationals depends on subtle philosophical points that have no possible proof or disproof and usually get glossed over. Accepting that philosophy also leads to the conclusion that not only do numbers which can in no way ever be represented exist, but there are more of them than numbers which we can explicitly name. Now I ask you, in what sense do they REALLY exist?
If so, here's a simple argument: If you have N rational numbers and I have K irrationals to start with, I can produce roughly N*K additional irrationals. Since we know at least two irrationals (pi and e) we can make at least twice as many irrationals as rationals.
0 <-> 1
1 <-> 3
2 <-> 5
:
I'm curious, how?
As 1/3 - exactly as it's on your screen. All rational numbers can be represented exactly.
Is possible to convert to rationals in calculations?
So if I do:
1/3 + 4 + sum / total it record values properly?