Prove [0,1) is of cardinality equal to (0,1]

Uriah Molina

Uriah Molina

Answered question

2022-11-08

Let A = [ 0 , 1 ) , B = ( 0 , 1 ] , C = ( 0 , 1 )
Prove A is of cardinality equal to B by using Glueing Lemma to 'glue together' the identity function idC and some appropriate bijective function.

Answer & Explanation

Ismael Wilkinson

Ismael Wilkinson

Beginner2022-11-09Added 13 answers

The glueing lemma for two maps:
Lemma. If A = A 1 A 2 and B = B 1 B 2 are decompositions (that is A 1 A 2 = B 1 B 2 = ), and f i : A i B i are bijectons for i = 1 , 2, then f = f 1 f 2 is a bijection A B
Here A 1 = B 1 = C and f 1 = i d C (L should be a typo).

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