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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?
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