Why can we change lim n→∞ to lim x→∞?

[@isaac0989]

Amazing, I've been looking for this explanation for almost 2 years. In 1st year college I asked one calculus professor about this, but he was very old, did'nt understand me and got upset, then just throw me the equivalence of continuity of a function in terms of sequences and said "I can see you don't study". Who knew that I would find the answer on KZbin years later

[@MyOneFiftiethOfADollar]

That just proves your teacher did not understand it well enough to explain answer to an excellent question which this video lucidly covers.

[@lexinwonderland5741]

Thank you for the counter-example to the reverse argument! That was 100% what I was watching for, though I stayed thru the whole video ofc! All in all, great content as always, keep up the great work:)

[@jperez7893]

So L is the target, epsilon is the error range, M is your aim point, and delta is the discrepancy of your aim contributing to the error and vice versa. You can fine tune your aim to the target, L, using x, but you are constrained when aiming at the target if you can only use set adjustments, n.

[@nasim09021975]

Very good explanation indeed 😊 Real Analysis and Complex Analysis are truly 2 of the most beautiful subjects in higher mathematics 🧮 Keep up the great work 👍

[@Akanksha4v]

Thank you for your explanation it really helped a lot 🙏🙂

[@michaelbaum6796]

Thanks a lot, very good explanation 👍

[@strikeemblem2886]

very clear! take my like

[@andrewgraybar4984]

When you graduate, another degree? Or, begin a career?

[@alexdemoura9972]

Excellent video, thanks.

[@claycurry5782]

Mathematics set aside, ur brows are fine as hell. No offense. Have a good day.

[@MyOneFiftiethOfADollar]

Excellent illustrative choice of functions! Since sin(2nPi) = 0 for all integers n, limit of constant equals the constant applies since n is a natural number in the limit statement. f(n)= sin(2nPi) f(n)-L=0 < Epsilon for all n Something like this used in proof that harmonic series diverges if one interprets 1/n is height of rectangle of width 1. Nice video

[@tsunningwah3471]

濕

[@tsunningwah3471]

god

[@tsunningwah3471]

ddx

[@magma90]

n is not specifically an integer and x is not specifically a real number. You have to set x∈ℝ for x to be a real number. x is just a variable, not specifically a real number. However, very good video. Thanks.

[@MuPrimeMath]

Yes, the fact that n typically denotes an integer and x typically denotes a real number in this context is a convention.

[@magma90]

@@MuPrimeMath ok