Once Upon A Winter - Selective Depression In Chase of The Big Bang [Full Album] 

It's an excerpt from a Numberphile episode featuring James Grime: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-elvOZm0d4H0.html. To be honest, I freaked out a bit when I heard it while I was listening to the album in background.

Well, this is essential in higher mathematics. When evaluating a function's stability it's needed to access if it can converge to a value as time increases. I could go on and on or I could refer you to the class of one of the greatest professors alive, Dr. Seiichi Nomura. Function e^x is the fastest to reach infinity and log(x) is the slowest. I hope you already learned this(and much more) in 3 years.

@@atulshrotriya3756 sorry for ranting a bit here, but reading that made me hurt... First of all, they are not talking about asymptotic behavior of functions or limits or things like that, they are talking about different sized infinite sets themselves. E.g. the fact that there is infinitely many natural numbers, infinitely many rational numbers, infinitely many real numbers. However the catch is that there are just as many natural numbers as rational numbers, those infinities are the same size, however there are MORE real numbers than natural numbers, i.e. the set of real numbers is bigger than the set of natural numbers. While the set of rational numbers is only as big as the set of natural numbers. Read up on cardinal numbers for more details. Secondly "e^x is the fastest to reach infinity", no. e^x grows towards infinity but it doesn't reach infinity, for every real x that is a finite number just as log(x) is a finite number for every (positive) real x. What you can say is that e^x grows faster than log(x) or to put it differently, e^x / log(x) tends towards infinity. However even then e^x is neither the fastest nor is log(x) the slowest growing function. Already e^(e^x) is a counter example as that clearly grows faster than e^x. And you can go a lot bigger, some functions even grow faster than any computable function, the most famous one is probably the busy beaver function.

@@myname356 I feel you man, sometimes it hurts in life. I wasn't talking about types of infinity. I expected him to have read about alef etc. I was talking about reaching infinity. What you say is correct. As per your example, in e^(e^x) I can consider e^x as another function of x say f(x) and then it will come to the same form and I was talking about 'general functions' which are directly related to physical phenomenon. Maybe you know your mathematics but I know mine too. And it will reach infinity if you can go to infinity, doesn't matter if you practically can or cannot, it's an assumption. For example, when dealing with very small numbers, we say that they are 0, when dealing with small theta, we assume that sin(theta)=theta. I've done my bachelor's in engineering and currently doing a masters so I can tell you that these concepts don't arrive before graduate level. Still, I'm not a mathematician and I might have made a mistake up there.

@@atulshrotriya3756 no, you don't reach infinity. That's the whole point. It even says in the excerpt on this very album: Infinity is not a number, it's a concept. You can look at what your function does as x approaches infinity. But x can't reach infinity. Now to be fair you can look at the limit as x goes to infinity. So sometimes you can make sense of lim x -> oo : f(x). But not always, f doesn't have to converge, simply look at f(x) = sin(x), it diverges for x -> oo. Besides, mathematics isn't concerned about practicality or physical phenomena. It is concerned about starting out with certain axioms and seeing what follows from them. As for "we say that small numbers are 0", maybe you engineers do that but no mathematician would ever say that sin(x) = x for small x. They'd maybe say sin(x) ≈ x. More likely they would say that sin(x) = x + O(x^3).

I heard "A Gallant Gentleman" from We Lost The Sea, myself. But it's a good track nonetheless!

Go check out "He films the clouds pt 2" by Maybeshewill. Ther's a surprise for you.

Worldhaspostrock Thank you!!!

thought my youtube decided to randomly autoplay Numberphile for a second...

I feel your pain...

I feel your joy...

I was looking through the comments to see if anyone wrote about that. Was going to write about it myself)) Nice to have you)

Extremely similar.

I know what you mean. That guitar riff totally reminded me one song from the earlier maybeshewill album.

remind me of he films the coulds pt.2 :D

Same here, I think that maybeshewill influences is very suspicious

it's almost identical. It's excellent to listen to, but too close

that's it, you're right. And sure that's a good thing.. for a moment it gives you a strange feeling that comes somewhere from the past.. then you realize it's a different album and you smile..

kokomo for the win

Artist: Once Upon A Winter (Greece) Album: Selective depression in chase of the Big Bang (2017) onceuponawinter.bandcamp.com

Rodolfo Rodrigues

Rodolfo Rodrigues What?