Homework SourseShow that there is a correspondence between the two interval
Show that there is a correspondence between the two intervals [0,1) and [0,1].
Show that there is a correspondence between the two intervals [0,1) and [0,1].
Show that there is a correspondence between the two intervals [0,1) and [0,1].
Solution
Let, S=[0,1)
T=[0,1]
Let, {an}={1/2,1/3,1/4...} be sequence in S
and {bn}={1,1/2,1/3,} be sequence in T
a_n=1/(n+1)
b_n=1/n
So there is a bijection from an to bn
f(an)=bn
So we have the bijection from [0,1) to [0,1]
g(x)=x if , x in S-{an}
else
g(an)=bn
![Show that there is a correspondence between the two intervals [0,1) and [0,1]. Show that there is a correspondence between the two intervals [0,1) and [0,1]. S](/WebImages/29/show-that-there-is-a-correspondence-between-the-two-interval-1082110-1761568435-0.webp "Show that there is a correspondence between the two intervals [0,1) and [0,1]. Show that there is a correspondence between the two intervals [0,1) and [0,1]. S")
