Cauchy General Principle of Convergence of a Sequence and one Problem by M. Arokiasamy

[dmcavinath]

Thank you sir for spending time for us, such a clear cut explanation and you made easy to understand. Once more, Thank you sir 👍🏻🤝👏

[roopachinnam]

Such a nice explanation sir. It was totally clear

[praveenyadavalli]

Wonderful Sir, step by step good construction of this lengthy theorm.

[gurramgayathri]

Nice explanation sir easy to understand

[Naveenbabuborugadda]

This is for 7:12
Sir if I take ε= then
ε/2 = may be makes a huge difference between small difference of the sequence terms.
I mean infinitely many terms of the sequence may lies between and
If we take ε as it self for all infinitely many values of n rather than ε/2 a new epsilon is introduced at the end of the theorem i.e 2 times of the ε
we take at the initial theorem for the difference between sequence terms ( | a suffix n+p - a suffix n|)<2ε
Especially 2ε maybe necessary to alternative converging sequence for
|a suffix n+p - a suffix n|

[dpcnagaharathi]

Good explanation sir I can understand the concept tq sir

[Naveenbabuborugadda]

For 7:12
*. if we compare 1 and 2 with ( large number)

1 and 2 looks like they are very very small but 1≠ 2 ( 1 is never equal to 2)
* Similarly Ɛ is very very small and
Ɛ/2 is also very very small positive real number but Ɛ≠Ɛ/2 ( Ɛ is not equal to Ɛ/2 for limit of a sequence)
* Hence, for given Ɛ >0
| a suffix n+p –a suffix n | < 2Ɛ

[Naveenbabuborugadda]

You told ε is very small and taken
ε/2 at 7:12 and in the example you have taken ε=1/2 and I think 1/2 is not very small then why don't you take ε itself in the theorem if you take ε itself you will get 2ε at the end of the theorem. Why don't you represent that 2ε as a ε'
ε' is different from ε there is the difference exists. ε' is two times the ε we take.