write out a proof using cardinality someone else gave me an

write out a proof using cardinality.. someone else gave me an answer using isomorphism but I don\'t think that\'s what we are supposed to do because we haven\'t learned that yet. please help!!

la.1 Let a ar db,k. Icalnumer ELAC b. that-Cab attu as a

Solution

Cardinality is the no. of elements present in the set.

So,

(a,b) is the subset of [a,b].

[a,b]=(a,b)+{a,b}.

As we know the set (a,b) contains all the real nos. between a & b. And the no. of real numbers present between 2 numbers are infinity.

|[a,b]|=|(a,b)|+|{a,b}|

=>|[a,b]|=|(a,b)| (Infinity + 2 = infinity)