Is e + Pi irrational?

[PlutoTheSecond]

Similarly, you can demonstrate that at least two of e+pi, e-pi and e*pi must be irrational.

[jacobhawthorne]

Please continue making these amazing videos!

[ffggddss]

Interesting, but useless fact: e + 2π is very close to 9.

[vermillion]

Love the format. Reminds me of Numberphile a bit!

[charlesbromberick]

I can tell you: e + pi is as irrational as hell, in fact I call it Nora after my last girlfriens who was one crazy broad.

[patrickwienhoft]

Am I the only one who has some real trouble deciphering his letters? I never would've guessed his p is a p, if he didn't say it. :D

[TheDiederikdehaan]

nice to see someone else writing x exactly the same way i od ;)

[julioezequiel]

You got a fan from Brazil!!
Keep doing this nice work :D

[zanti]

As this proof's only requirement about e and π is that they are both transcendental, it would follow that this is true for any two transcendental numbers, i.e. given a and b are both transcendental, then a + b and a × b can't both be rational.

[lucianosantos-qbhw]

I bet on the irrationality of e + pi. But after hearing this video, no. Thanks

[nikhiljagtap]

Bernoulli used e to find the complex interest on 1 if the interest is compounded infinite times in one year. He figured it out that it will be between 2 and 3, but not exact value. Euler evaluated the value in terms of factorials of numbers.

[ChumX]

Chances are both e+π and eπ are irrational. After all, most numbers are. The interesting part is the difficulty of proving such an apparently simple statement. Imo, it would be a mathematical miracle if any of these would be rational.

[mathsmoica]

Really good video !
Clear&Concise

[morgengabe]

Deleted my comment after re-watching. I was not listening lol.
Your channel's actually pretty cool. I like what you're doing by distributing and informing people about important papers. Keep up the good work!
Es Brazileiro?

[Quantris]

a) Is there a way to prove without relying on transcendentalness?
b) What can we say about transcendentalness of e + pi or e*pi? Any result like "if it is irrational, it must also be transcendental"?

[douro]

e is also the sum from n=0 to infinity of 1/n!. I almost never see this mentioned.

[kevina]

Fun fact: if you take e hexatated to pi, you get an insanely large number that might be irrational

[Pancake]

I understood what was going on, yay! Great work with the video

[zanti]

While this isn't a proof, it's obvious that e+π is irrational. The reason for this is because if e+π is rational, then the decimal expansion for e+π would eventually start repeating and repeat forever. So let's say the decimal expansion for e+π starts at the nth digit of e+π and continues for a length of k, at which point it starts repeating. Now take the digits of π starting at the nth digit for a length of k and make an integer out of it. (To clarify, if we make an integer out of the 3rd through 6th decimal digits of π = 3.1415926.... we'd get 1592.) Do the same for e, then add the two integers. This sum would have to equal or "nearly equal" the sum you get if you take the corresponding digits of π and e for any other range of repeating digits in e+π, of which there are infinitely many. (By "nearly equal" I mean the numbers may differ by one or two digits due to carryover.) If the digits of π and e are random, i.e that both numbers are normal, then we know for certain this can't happen, but π and e haven't been proven to be normal, either.

[gheffz]

I will dare at a guess! .... *BOTH* π + _e_ and π * _e_ are irrational !!! _(How's that for a stab in the dark!!!)_