Math Is Fun Forum
Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °
You are not logged in.
- Topics: Active | Unanswered
#1 2010-04-18 17:52:38
- cxc001
- Member
- Registered: 2010-04-09
- Posts: 17
Set Theory: Prove the set of complex numbers is uncountable
How to prove the set of complex numbers is uncountable?
Let C be the set of all complex numbers,
So C={a+bi: a,b belongs to N; i=sqrt(-1)}
--------------------------------------------------
set of all real numbers is uncountable
open intervals are uncountable
set of all irrational numbers is uncountable
--------------------------------------------------
Offline
#2 2010-04-18 19:44:27
- JaneFairfax
- Member
- Registered: 2007-02-23
- Posts: 6,868
Re: Set Theory: Prove the set of complex numbers is uncountable
It contains the subset ℝ which is well known to be uncountable. Is that proof enough?
Offline
#3 2010-04-19 07:19:38
- cxc001
- Member
- Registered: 2010-04-09
- Posts: 17
Re: Set Theory: Prove the set of complex numbers is uncountable
Yes, R (set of all real no.) is a subset of C (set of all complex no.)
R={a+0i: a is real no}, C={a+bi: a,b are real no}
R is uncountable, therefore C is also uncountable
Offline