Hey Wrath, I'm currently taking Fundamental Analysis I. Your videos have helped me a lot in understanding abstract concepts and how to do proofs. They’re clear and concise. Keep up the good work!
Hello, thanks for this proof, I am looking forward to not being forced to use epsilon-delta :D . I came here from your video on function limits - really helpful as well. I'd have a question on the
I am a bit confused with second direction of the proof. By assuming the limit of f(x) is not L and finding a sequence that defies the rule, isn't that a proof by contrapositive?? I understand the steps in the proof well but i don't understand how it a proof by contradiction.
Contrapositive is a special form of contradiction, where the hypothesis is true and we derive *the* contradiction that is the negation of that hypothesis. We know what type of contradiction we aim to, whereas in many proofs the contradiction isn't exactly the hypothesis (for example the irrationality of sqrt2, where the contradiction comes from deriving p and q share a factor of 2, though p/q are in lowest terms)
Hey Wrath, I'm currently taking Fundamental Analysis I. Your videos have helped me a lot in understanding abstract concepts and how to do proofs. They’re clear and concise. Keep up the good work!
So glad they've helped, thanks for watching! Let me know if you have any questions and good luck in your course!
I second this
Thank you Sir for your very clear explanation ❤
highschooler here, helped a lot during exams. thanks!
You're very welcome!
Hello, thanks for this proof, I am looking forward to not being forced to use epsilon-delta :D . I came here from your video on function limits - really helpful as well. I'd have a question on the
THIS HELPED SO MUCH!! TYSM
can you make a video about protractors
I could not grasp the part where you link the "negated definition of limit of a function " to sequence at 8:12
Would appreciate any help...
Awesome Video! Helped a lot!
Glad to hear it, thanks for watching!
I am a bit confused with second direction of the proof. By assuming the limit of f(x) is not L and finding a sequence that defies the rule, isn't that a proof by contrapositive?? I understand the steps in the proof well but i don't understand how it a proof by contradiction.
Contrapositive is a special form of contradiction, where the hypothesis is true and we derive *the* contradiction that is the negation of that hypothesis. We know what type of contradiction we aim to, whereas in many proofs the contradiction isn't exactly the hypothesis (for example the irrationality of sqrt2, where the contradiction comes from deriving p and q share a factor of 2, though p/q are in lowest terms)