What percentage of real numbers are transcendental?

Dec 2013
28
0
Real numbers can be separated into 2 sets, the set of algebraic numbers and the set of transcendental numbers. What's the percentage of both sets?
 

skipjack

Forum Staff
Dec 2006
21,481
2,470
What are your estimates?
 

v8archie

Math Team
Dec 2013
7,713
2,682
Colombia
Hint: one of the sets is countable, the other isn't.
 

CRGreathouse

Forum Staff
Nov 2006
16,046
936
UTC -5
Asymptotically the transcendental numbers have measure 1 and the algebraics have measure 0, so 100%/0% would be reasonable.
 

Country Boy

Math Team
Jan 2015
3,261
899
Alabama
Why in the world would you think you could compare infinite sets using "percents"?
 

CRGreathouse

Forum Staff
Nov 2006
16,046
936
UTC -5
Why in the world would you think you could compare infinite sets using "percents"?
In this case we can because both are measurable. But you're right, usually this isn't possible.
 
May 2015
109
5
Varanasi
It's really impossible to tell, number are infinite.