0] Prove that is the identity element for addition of ordinal numbers, that is, for any ordinal A, we have 0 + 1 = +0= X. 0 Prove that I is the identity element for multiplication of ordinal numbers, that is for any ordinal X, we have 1X = X1 X. Prove: If each , 1 € P, is a finite ordinal, then 4, + 12 + ... - =w. C/ Prove: Let X be any infinite ordinal number. Then :=+, where is a limit number and is a finite ordinal State whether each of the following statements about ordinals is true or false; if it is true prove it, and if it is false give a counterexample: (a) 0then <+# (h) in 60, then <+.