Real Analysis | An important property of integration.

We prove that integrals of bounded functions can be split up by splitting the intervals of integration.
Please Subscribe: www.youtube.co...
Merch: teespring.com/...
Personal Website: www.michael-pen...
Randolph College Math: www.randolphcol...
Randolph College Math and Science on Facebook: / randolph.science
Research Gate profile: www.researchga...
Google Scholar profile: scholar.google...
If you are going to use an ad-blocker, considering using brave and tipping me BAT!
brave.com/sdp793
Buy textbooks here and help me out: amzn.to/31Bj9ye
Buy an amazon gift card and help me out: amzn.to/2PComAf
Books I like:
Sacred Mathematics: Japanese Temple Geometry: amzn.to/2ZIadH9
Electricity and Magnetism for Mathematicians: amzn.to/2H8ePzL
Abstract Algebra:
Judson(online): abstract.ups.edu/
Judson(print): amzn.to/2Xg92wD
Dummit and Foote: amzn.to/2zYOrok
Gallian: amzn.to/2zg4YEo
Artin: amzn.to/2LQ8l7C
Differential Forms:
Bachman: amzn.to/2z9wljH
Number Theory:
Crisman(online): math.gordon.edu...
Strayer: amzn.to/3bXwLah
Andrews: amzn.to/2zWlOZ0
Analysis:
Abbot: amzn.to/3cwYtuF
How to think about Analysis: amzn.to/2AIhwVm
Calculus:
OpenStax(online): openstax.org/s...
OpenStax Vol 1: amzn.to/2zlreN8
OpenStax Vol 2: amzn.to/2TtwoxH
OpenStax Vol 3: amzn.to/3bPJ3Bn
My Filming Equipment:
Camera: amzn.to/3kx2JzE
Lense: amzn.to/2PFxPXA
Audio Recorder: amzn.to/2XLzkaZ
Microphones: amzn.to/3fJED0T
Lights: amzn.to/2XHxRT0
White Chalk: amzn.to/3ipu3Oh
Color Chalk: amzn.to/2XL6eIJ

[@marekkryspin8712]

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!

[@masterkavi619]

thank you sir

[@algorithmo134]

Hi can you do a video on proof of inverse function theorem, implicit function theorem, and contraction mapping theorem? Thank you sir!

[@manasbindhani7915]

Thank you

[@user-en5vj6vr2u]

I see him post, I click; I see inequality and epsilon, I leave

[@stuartyeo5354]

Haha nice

[@goodplacetostop2973]

13:28

[@braydenhascup1560]

I see you post I click

[@TonyPeperoni248]

yo that speed at 3:36

[@legendarydisciplegaming4316]

Is there a soln. To this eqn. X⁸+ qx⁶ - x⁵ + 2qx⁴ + px³ - 3q/4

[@OuroborosVengeance]

Peanut

[@djvalentedochp]

cool

[@eminvahid3976]

👍🏻

[@Reliquancy]

Is real analysis at some point going to get beyond proving stuff that I was fine taking as intuitively obvious in calculus?

[@Reliquancy]

@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...

[@Reliquancy]

@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.

[@Reliquancy]

@Jessen Well, there’s sine. Is there one that’s always positive valued like that?

[@Reliquancy]

@Jessen That is interesting but I was thinking always positive as in it couldn’t be 0 anywhere...

[@Reliquancy]

@Jessen Cool thanks! I guess there’s a whole world in that starting line of calculus theorems that are “for continuous bounded continuously differentiable...”

[@danconcep]

Where did we use that f is bounded in the proof? I must have missed it.

[@okra_]

we've only dealt with integrability on bounded functions so far

[@danconcep]

@@okra_ thanks