Welcome to our community

Be a part of something great, join today!

Prove that the interval A = [0 , 2) has the same cardinality as the set B = [5 , 6) U [7 , 8)

KOO

New member
Oct 19, 2013
19
Prove that the interval A = [0 , 2) has the same cardinality as the set B = [5 , 6) U [7 , 8) by constructing a bijection between the two sets

Attempt:

x ↦ x + 5 for x ∈ [0 ; 1)
x ↦ x + 6 for x ∈ [1 ; 2)

What to do next?
 

Fernando Revilla

Well-known member
MHB Math Helper
Jan 29, 2012
661
What to do next?
Prove that $f:[0,2)\to [5\color{red},\color{\black}6)\cup [7,8)$
$$f(x)=\left \{ \begin{matrix} x+5& \mbox{ if }& x\in [0,1)\\x+6 & \mbox{ if }&x\in [1\color{red},\color{\black}2)\end{matrix}\right.$$
is injective and surjective.
 
Last edited:

KOO

New member
Oct 19, 2013
19
Prove that $f:[0,2)\to [5.6)\cup [7,8)$
$$f(x)=\left \{ \begin{matrix} x+5& \mbox{ if }& x\in [0,1)\\x+6 & \mbox{ if }&x\in [1.2)\end{matrix}\right.$$
is injective and surjective.


Did you mean [5,6) and not [5.6)?

Also, [1,2) and not [1.2)?

Thanks!
 

Fernando Revilla

Well-known member
MHB Math Helper
Jan 29, 2012
661