One problem of Mathematical

Induction

04/10/23 SANDEEP MCA-IVTH SEMESTER

2

Here is the problem :

Theorem: All the elements in any set must be identical.

Proof:

Induction Basis:

For any set with zero or one elements, The statement is true.

04/10/23 SANDEEP MCA-IVTH SEMESTER

3

Hypothesis:Let it be true for all the sets with

n-1 elements.

Induction Step:Let S be a set containing n

elements. And a be an element of S. Writing S= S1 U S2.

S1 and S2 have n-1 elements each and each contain a.

Thus it is true for n also.Hence Proved.

04/10/23 SANDEEP MCA-IVTH SEMESTER

4

Query ?

How can this be possible?