Define the injections f:A -> B by f(a)=4a and g:B -> A by g(b)=b. Find the set Cand the ultimate bijection h

(1)-Let A be the integers and let B be the even integers. Define the injections f:A -%26gt; B by f(a)=4a and g:B -%26gt; A by g(b)=b. Find the set C and the ultimate bijection h.





(2)-Show that any real interval [a,b] with b%26gt;a has the cardinality of the continuum.

Define the injections f:A -%26gt; B by f(a)=4a and g:B -%26gt; A by g(b)=b. Find the set Cand the ultimate bijection h
I assume the ultimate bijection h(x)=f(g(x)) and C is the range of h. Accordingly,


h(x)=f(g(x))=4g(x)=4x


C=h(A)=h(integers)


={...,-8,-4,0,4,8,...}


=multiples of 4


h is injective because it is the composition of two injections


h is surjective because C=h(domain of h)=h(A)


Thus h is a bijection.
Reply:What is the set C supposed to be? You haven't defined it.

forsythia