Usually I don't pick on notation, but it is important here. You're talking about the Darboux integral not Riemann integral. Riemann integral is defined by the limit of Riemann sums and does not require the definition by sup and inf. Ultimately, both definitions are equivalent to each other so everything is correct, but technically the construction of the integral Riemann is different. Great movie as always!
@Jessen So what’s an example proof like that? Every video he’s done in this series so far has been kind of proving just what your intuition wiuld tell you...
@Jessen Well, I came across the Weierstrass function looking up something from one of these videos. But I think I see what you’re getting at that the existence of such a thing definitely isn’t intuitively obvious. I hadn’t put together yet that that was beyond something you would assume in calculus.
@Jessen Cool thanks! I guess there’s a whole world in that starting line of calculus theorems that are “for continuous bounded continuously differentiable...”
Usually I don't pick on notation, but it is important here. You're talking about the Darboux integral not Riemann integral. Riemann integral is defined by the limit of Riemann sums and does not require the definition by sup and inf. Ultimately, both definitions are equivalent to each other so everything is correct, but technically the construction of the integral Riemann is different. Great movie as always!
thank you sir
Hi can you do a video on proof of inverse function theorem, implicit function theorem, and contraction mapping theorem? Thank you sir!
Thank you
13:28
yo that speed at 3:36
Is there a soln. To this eqn.
X⁸+ qx⁶ - x⁵ + 2qx⁴ + px³ - 3q/4
I see you post I click
I see him post, I click; I see inequality and epsilon, I leave
Haha nice
👍🏻
cool
Peanut
Is real analysis at some point going to get beyond proving stuff that I was fine taking as intuitively obvious in calculus?
@Jessen So what’s an example proof like that? Every video he’s done in this series so far has been kind of proving just what your intuition wiuld tell you...
@Jessen Well, I came across the Weierstrass function looking up something from one of these videos. But I think I see what you’re getting at that the existence of such a thing definitely isn’t intuitively obvious. I hadn’t put together yet that that was beyond something you would assume in calculus.
@Jessen Well, there’s sine. Is there one that’s always positive valued like that?
@Jessen That is interesting but I was thinking always positive as in it couldn’t be 0 anywhere...
@Jessen Cool thanks! I guess there’s a whole world in that starting line of calculus theorems that are “for continuous bounded continuously differentiable...”
Where did we use that f is bounded in the proof? I must have missed it.
we've only dealt with integrability on bounded functions so far
@@okra_ thanks