Post by Give: e

Most of my work is not particularly quantitative - I work in a restructuring firm where we do a lot of cash flow modeling, advising management and boards, negotiating with lenders and equity sponsors. The standard technical skills you need are building an integrated financial model, doing some DCFs and multiple valuations, calculating some leverage and coverage ratios across the debt capital structure, and making convincing presentations. I just love nerding out in my free time or when work demands it and exploring finance-related quantitative topics, reading and writing articles… for my personal entertainment and continuing education

do you write on Seeking Alpha by any chance?

no, never have

BS. Give the proof or STFU.

step aside, rookie

^ Ha ha, you don’t know the proof do you.

Sure I don’t. Get it started and show some work, we’ll figure it out together

Lay off Mobius Striptease. He’s one of the very few that gets my astro-physics jokes.

I will lay off if he puts up the proof. What is this “Get it started and show some work, we’ll figure it out together” cop-out?

Mobius is a well respected poster here. He doesn’t want to give out the proof too easily and probably doesn’t respect being bossed around.

Proof or it didn’t happen, Mobius. It’s like an extremely nerdy version of “pics or it didn’t happen”.

There’s definitely a trick I’m missing:

e^pi < pi^e : [test for inequality, reverse if proven false]

ln(e^pi) < ln(pi^e) : log function is monotonic increasing, so inequality is maintained

pi * ln(e) < e * ln(pi)

pi < e * ln(pi) : ln(e)=1

pi/e < ln(pi)

Now I get stuck. pi/e is > 1. Pi > 1, so ln(pi) > 1, so I can’t say for sure that pi/e < ln(pi) by using positive and negative numbers. But if I can’t use an approximation to calculate e^pi, why would I know what ln(pi) is.

I could try a change of base to get pi to drop out, but it doesn’t seem to go anywhere:

pi/e < log_pi(pi)/log_pi(e) = 1/log_pi(e)

e/pi > log_pi(e)

log_pi(e) is between 0 and 1, but so is e/pi, so it doesn’t seem to go anywhere.

Can I have a hint???

Wouldn’t it be easier just to enter 3.1416^2.7183 into the calculator, then enter 2.7183^3.1416 into the calculator, and see which number is greater?

It sounds like you guys are doing Obamacore-type stuff.

I’ve done that (and posted it earlier in the thread), but AfricaFarmer and MobiusStriptease suggested there’s a nicer analytic solution.

It would be, just like it would be easier for me enter my W-2 in H&R block rather than pay some tax CPA to monkey around with the numbers. But occasionally they find deductions that the tax software missed. Sometimes an analytical solution provides an insight of some sort, or level of understanding that sits at the back of your brain until you can apply it to something useful. Sometimes it’s just for fun and mental exercise. Also in my opinion, nerding out on a quant topic is not any nerdier than nerding out on a tax regulation or obscure FASB rule, and both can be indirectly relevant to finance.

Nice. The trick next is to think in terms of functions and apply some basic calculus: f(x)=x, g(x)=e*ln(x). Clearly f(e)=g(e). This equality is a good start that will allows us to compare f(pi) and g(pi) by looking at which function is “faster”.

That’s respectable. So you must be one of the rare people with quant skills with people skills. I’m increasingly realizing how rare the combo is

^ I’m still not convinced that exists.

OK, I will bite.

f(x) = x => f’(x) = 1

g(x) = e ln (x) => g’(x) = e/x

At x = e, f(x) = g(x)

g’(x) < f’(x) for all x > e, so the integrals will be as well, ergo

g(pi) < f(pi) or e ln pi < pi ln e => pi^e < e^pi.

Nice.

bchad: I clearly don’t react well to the expository style. I am a busy guy

This is certainly true. I might nerd out with you, but I know nothing about quant. If the math is any higher than college algebra, I’m lost.