"given that proposition "something = epsilon" is clearly false" - where is it given or justified? Without justification, this simply equates to hand-waving and unrigorous math.
@@hakus4600 Actually, equality is cleary false beacuse |x-c| < delta, it was given three lines above. I totally agree that "A is true" is better conclusion than "A or B is true, given that B is false". But with the latter as statement, you can conclude the former. Argument is totally correct.
@@nicolasg.b.1728 Great, if you write out exactly where your "clearly" comes from as you just did, I as a grader will give you full mark on this. Otherwise, I'll take away 1 point or 2 due to the lack of rigor.
Love the proof of the power rule! It was always so mysterious back in calculus, I thought it was actually empirical when I first learned about it. Great to see it in concrete terms!
@@nicolasg.b.1728Notice in the definition on the previous board, you would need strict inequality i.e. the absolute value of f(x)-f(c) is strictly bounded by epsilon in order to prove uniform continuity. Yes what you wrote is a true statement, but simply not sufficient to prove uniform continuity.
Once you have a true statement, lets say A, and you add another statement B with an OR, the statement "A or B" is also true, no matter B's truth value. That is a rule of inference called "disjunction introduction" or "addition". So, if you know that "10 is less than 100" is true, then "10 is less or equal to 100" is also true. Thus, as both propositions contained your suficcient condition, then both conclusion serve your purpose. Yeah, is cumbersome. But is logically correct.
@@nicolasg.b.1728 I do not think you are grasping the gist of my original comment. Try answering this- given the proposition: "A is true" implies "X is true", does it follow that "A or B is true" implies "X is true"?
@@hakus4600 Keep pushing, you're near the answer. Try to follow closely mi above analogy: What happen when you KNOW that B is not true (i.e., you KNOW that "10 is equal to 100" is false)? Then you can conclude that "10 is less than 100" is true. This form of argumentation is called disjunctive syllogism. Take a look at it. Prof. Rodriguez's argument is totally correct.
Can't believe he mentioned Borat, I love those little tidbits during these lectures.
Hey self-learners! Prof. Rodriguez made a conclusion at 27:40 that may cause confusion. He said "something
"given that proposition "something = epsilon" is clearly false" - where is it given or justified? Without justification, this simply equates to hand-waving and unrigorous math.
@@hakus4600 Actually, equality is cleary false beacuse |x-c| < delta, it was given three lines above. I totally agree that "A is true" is better conclusion than "A or B is true, given that B is false". But with the latter as statement, you can conclude the former. Argument is totally correct.
@@nicolasg.b.1728 Great, if you write out exactly where your "clearly" comes from as you just did, I as a grader will give you full mark on this. Otherwise, I'll take away 1 point or 2 due to the lack of rigor.
Love the proof of the power rule! It was always so mysterious back in calculus, I thought it was actually empirical when I first learned about it. Great to see it in concrete terms!
Love this
Finally, the almighty derivative, I've been waiting for this!
Very helpful lesson. Thank you Professor..🙏🙏
at 27:40 I believe there's a typo: you should have a "
No, it is indeed correct. You can say "10 is less or equal to 100".
@@nicolasg.b.1728Notice in the definition on the previous board, you would need strict inequality i.e. the absolute value of f(x)-f(c) is strictly bounded by epsilon in order to prove uniform continuity. Yes what you wrote is a true statement, but simply not sufficient to prove uniform continuity.
Once you have a true statement, lets say A, and you add another statement B with an OR, the statement "A or B" is also true, no matter B's truth value. That is a rule of inference called "disjunction introduction" or "addition". So, if you know that "10 is less than 100" is true, then "10 is less or equal to 100" is also true. Thus, as both propositions contained your suficcient condition, then both conclusion serve your purpose. Yeah, is cumbersome. But is logically correct.
@@nicolasg.b.1728 I do not think you are grasping the gist of my original comment. Try answering this- given the proposition: "A is true" implies "X is true", does it follow that "A or B is true" implies "X is true"?
@@hakus4600 Keep pushing, you're near the answer. Try to follow closely mi above analogy: What happen when you KNOW that B is not true (i.e., you KNOW that "10 is equal to 100" is false)? Then you can conclude that "10 is less than 100" is true. This form of argumentation is called disjunctive syllogism. Take a look at it. Prof. Rodriguez's argument is totally correct.
Why at around 1:09 we can change the start and the end of the summation?
just 2 cases.
especially, f is inc OR f is dec
Spreading all the chalk 😅😮
He needs something better than that crayola chalk.