Proof: Constant Sequence Converges to its Constant Value | Real Analysis

Does a constant sequence converge? And if so, what does it converge to? As you'd expect, a constant sequence, where every term is equal to some real number c, converges to its constant value of c. We'll prove that constant sequences converge to their constant values in today's real analysis video lesson.
The math behind the proof is very simple. When we prove a sequence converges to a limit, we show that the sequence eventually gets within epsilon of its limit for any positive number epsilon. Of course, for our constant sequence equal to c at every term, it's always 0 away from c, since it is always equal to c, and so certainly c is its limit.
Real Analysis Playlist: • Real Analysis
Intro to Sequences: • Intro to Sequences | C...
Definition of the Limit of a Sequence: • Definition of the Limi...
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[@WrathofMath]

Hey folks, please forgive the number of cuts in this video. I filmed it after getting hardly any sleep, waking up sick, then doing a 4 hour long drive home to my math den.

[@aryanoak5355]

why is n greater than OR EQUAL to N and not just n greater than N like previous examples of convergent sequence proofs

[@vivekjha8688]

Late reply but hopefully you see that’s trivial to the definition. If “N” is a problem choose n > N + 1. When talking about convergence you just have to find some* N. Who cares if for some domain reason or else, if a finite subsequence doesn’t work as long as the distance becomes arbitrarily small after some “N”

[@mahmoudalbahar1641]

Thank you so much for this good video.

[@WrathofMath]

You're very welcome, it is my pleasure!

[@thenewdimension9832]

Beautifully explained 🥰🙏

[@WrathofMath]

Thank you!

[@yavuzcems]

thank you so much

[@WrathofMath]

My pleasure, thanks for watching!

[@armanrasouli2779]

I love your shirt :)

[@WrathofMath]

Thank you! It's very convenient with its pouch for dry erase markers and all!