Princess Cadance (Mi Amore Cadenza) Is Actually a Lot Better at Differential Calculus (and Other Assorted Fairly Complex Topics in Mathematics) than Anyone Would Have Reasonably Expected

by Lazauya

f(x) = exp(x) - x, (f^(-1))(x) = ?

"Not much."
"Huh? What was that Starlight?"
"What? Oh, sorry, Spike, just thinking out loud."
"Oh," Spike said finally as the two stared out into the distance from their perch on the hill.

Author's Note:

idk

Comments

[Needling Haystacks]

7902070
7900717

I think I said I had seen worse descriptions. XP A worse one would be maybe like "stuff expanded from stuff and then it kept doing that." Not completely incorrect (so it still qualifies as a description), but pretty bad. XP

Let's try a better one... "By tracing back motion now, we can conclude that the universe was once all in a point. By how light changes over time, we can tell that it expanded very rapidly at first, like a big explosion or bang."

That's my attempt to incorporate why we think the Big Bang happened. To really do a more complete description, it would involve either more sentences or run-on sentences, regardless of jargon.

[King of Kings]

7902126
25 weeks is my cutoff point for caring about comments left on this site. Besides which, no matter who said that, I now care a lot more about Sonic T. Hedgehog shippings than I do about that shipping. Primarily SonAmy and SonTails.

[Capacitor]

7902070
Not that I had any particular problem with the description, but...
Whatever jargon I like, you say? I'm by no means an expert, but I think I may have something neat and concise written down somewhere...

*interlude while I rummage through some notes*

There it is:
H²(t) = (da/dt a⁻¹)² = H²(0) ( Ωm a⁻³ + Ωγ a⁻⁴ + Ωκ a⁻² )
Here a(t) is the scale the universe relative to its current size, Ωm is characterized by nonrelativistic particles (matter), Ωγ by relativistic particles (light) and Ωκ by the space-time geometry of the universe (hyperbolic, spherical or flat).

Not a lot of detail, but that's cosmology for you. Things get very macroscopic, especially if you assume things like the weak field limit, homogeneity or isotropy.

[ShadTK]

F^-1 (x)= ln x + ln y, i think
Though something about that answer is feeling wrong

[Perteks]

Oh damn its dead ?