Awesome tutorial thx! With the first proof, thinking about it visually, can the "a" be anywhere on the number line - in between -1 and 1 or on either side? Also, why must ε ≤ 1 when the distance between -1 and 1 is 2? Your help would be much appreciated. thx
@@brightsideofmaths is it important to define a metric even before talking about convergence? I mean what | An - A | even means when we have no notion of a metric? I am so confused, how to study analysis, metric spaces, topology all together?
@@paulhowrang Yes, we define convergence with respect to a metric. However, the real numbers already carry the standard modulus/absolute value. We can use that to measure distances.
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Awesome tutorial thx!
With the first proof, thinking about it visually, can the "a" be anywhere on the number line - in between -1 and 1 or on either side? Also, why must ε ≤ 1 when the distance between -1 and 1 is 2?
Your help would be much appreciated. thx
We want to find a counterexample for epsilon :)
@@brightsideofmaths thanks!
what does n≥N means? i can't understand
I have a start learning mathematics series about that: tbsom.de/s/slm
@@brightsideofmaths is it important to define a metric even before talking about convergence? I mean what | An - A | even means when we have no notion of a metric?
I am so confused, how to study analysis, metric spaces, topology all together?
@@paulhowrang Yes, we define convergence with respect to a metric. However, the real numbers already carry the standard modulus/absolute value. We can use that to measure distances.