When Does Exponentiation Commute? (Part 1)

[@BrettEskrigge]

Hey I know that you may not have many subscribers or be getting many views on your videos, but I just wanted to say that your videos are amongst the most comprehensible videos that talk about more complicated forms of mathematics like this. And thank you for that Just keep on making awesome videos like this, and I'm sure that you'll get plenty for subscribers and views in the near future!

[@BrettEskrigge]

+Brett Eskrigge And also, Happy New Year!

[@Math_oma]

+Brett Eskrigge Happy New Year to you too and thanks for the compliment. This channel is still quite new and probably won't get as many subscribers as a channel about cat videos, but that's okay. As long as some people learn something from my videos or find a way to make it useful in real life, then I'm happy. As you can see, this video is adapted from that paper I sent you.

[@BrettEskrigge]

mdphdguy1 You're welcome Yeah, I noticed that. I saw some similarities between this video and that paper. Although I found the paper kind of hard to understand, for me this video was crystal clear Keep the good work up!

[@joaovitordb1270]

+Brett Eskrigge I also think that's an awesome channel! I learned set theory with his videos without having prior knowledge. The most comprehensible and complete videos that I found on youtube about that for beginners!

[@BrettEskrigge]

João Vitor Denardi Bosa I'm yet to watch those videos as I have been busy, but I will watch them hopefully in the near future. It's good to see this channel getting appreciation!

[@YahiaDesigner]

can't no matter what express my gratitude, keep it up, you're overly underrated, just great content.

[@Math_oma]

+Foxy I may not be very popular but my overarching goal (perhaps pretentious) is to make videos that will still be useful in 20+ year's time.

[@YahiaDesigner]

I have no doubt. could you possibly explain the Lagrangian version of the lambert W function shown as a series, I think that'd be absolutely helpful to know how to approximate it without the need of a computer. i.e: is there probably a way to calculate the W function by hand?

[@Math_oma]

+Foxy I'm not sure if that would merit a whole video but I'll consider returning to computational considerations of the W function. In another old video I made on the W function, I show how to compute it using Newton's method, so it can be calculated using a scientific calculator.

[@Jojo160992]

At 6:04 you took the 1/y-th power on both sides. Don't this produce an equation which is not equivalent to the previous one (especially if y is even, e.g. x^2 = 4 is not equivalent to (x^2)^(1/2) = 4^(1/2), i.e., x = 2)?

[@Jojo160992]

or, are we considering positive real numbers only?

[@Math_oma]

+Jojo160992 Yeah, just positives. I don't think there are any negative solutions anyway, so we aren't losing any solutions by doing what I did.

[@BigDBrian]

When you were computing pairs of x and y, after you calculated x, you could simply take your chosen value of t times x to get y, since as was originally defined, y = t*x

[@spudhead169]

Awesome, can you prove or disprove that there is a corresponding value of t using your parameterized functions for EVERY possible commutable value pairs of x, y?

[@MrPierreOB]

Hello would there be a way of finding only whole numbers for the x and y pairs?

[@jameswilson8270]

Very interesting! Thanks for sharing! Going to watch part 2 now!

[@esul4]

Thanks for the simple and clear explanation. Learnt a new concept today. I have a question: Since the parameter t relates x and y in a particular way (y = tx), wouldn't the set of x-y pairs thus obtained be smaller than the set of *all* (x,y) for which exponentiation commutes?

[@esul4]

Never mind, I was in a bit of a rush and missed the part where you said that parametrization was a way of taking a guess at the solution.

[@brendanmccann5695]

Great content! Wonderful, wonderful presentation! Thank you.

[@joseadolfogomezjimenez9181]

Amaizing. Very well explained.

[@RealLifeKyurem]

Was the equation y=tx at the start of the parameterization also guessed?

[@Math_oma]

+Aphrontic Alchemist It was guess/inspired.

[@saitaro]

Great video.