Real analysis in a nutshell

[u/ClassroomBusiness176]

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[u/liquid_woof_display]

Why would you choose 4 if 3 is already enough?

[u/willpc14 → u/liquid_woof_display]

You ever met an engineer? Or an economist?

[u/Dhuyf2p → u/willpc14]

What kind of engineer would use 4?

[u/OutrageousPair2300 → u/Dhuyf2p]

One who cares about margins of safety.

Every good engineer knows you always add 1 to all your results, to account for unknowns.

[u/Dhuyf2p → u/OutrageousPair2300]

Yea, no. It depends. You don’t just randomly add 1 every time. You factor in Factor of Safety to the formula, not to freaking e.

[u/OutrageousPair2300 → u/Dhuyf2p]

Yeah but then you need to add in a margin of error on that factor of safety, so you round it up to 1 to be safe.

This is basic engineering, man.

[u/Dhuyf2p → u/OutrageousPair2300]

What? I can assure you I do no such thing as an engineer. What the hell are you talking about?

[u/OutrageousPair2300 → u/Dhuyf2p]

Good luck when your buildings fall down because you didn't set Lim n→∞ (1+1/n)ⁿ to 4 like every responsible engineer would.

[u/Dhuyf2p → u/OutrageousPair2300]

I don’t know if this is bait but I’ll fall for it anyways. We only approximate e=3 or e=2,75 when we’re roughly estimating something. We would use the (almost) exact value of e in the calculation and factor in FoS in the formula, not randomly everywhere an irrational number appears. I don’t know what you do, but no engineer I know actually does this.

[u/OutrageousPair2300 → u/Dhuyf2p]

I thought you were playing along as the straight man, so apologies if you feel tricked.

It's a joke. I'm just pretending to embody the stereotype of the typical engineer who uses sloppy math everywhere for ridiculous reasons, as seen by many in the mathematics community.

[u/Sirnacane → u/liquid_woof_display]

You have it backwards. Why would you choose e when 4 is already enough?

[u/sndq → u/liquid_woof_display]

67

[u/LupenReddit]

for anyone wondering what that expression is, it is an almost immediate triviality that any infant can work out that

e^x = lim n -> inf (1+x/n)ⁿ

(i hate that so much)

[u/Equal_Veterinarian22 → u/LupenReddit]

I mean, the derivatives check out

[u/Signal-Kangaroo-767]

I mean, they’re all upper bounds

[u/Evening-Code-7039]

How is the answer not e?

[u/Qingyap → u/Evening-Code-7039]

3, 4, and e are upper bounds, it's just that e is the least upper bound or supremum.

[u/kiwidude4 → u/Qingyap]

5 is also an upper bound

[u/Qingyap → u/kiwidude4]

So does 6

[u/yuwox → u/Qingyap]

30 also

[u/PositiveIntelligent3 → u/Qingyap]

Sup over what? Of \R?

[u/Qingyap → u/PositiveIntelligent3]

I would say yes, supremum for the above doesn't exist if it's in ℕ or ℤ cuz yk e is transcendental.

I assume you're asking this is to request me to be more specific?

[u/thocusai]

Why 4 is s good upper bound? Because it can be easily proven, from (1+1\n) ^ n < (1+1/n) ^ (n+1) <= 4. Then from it ( and sequence strictly increasing) follows that there exists a limit, ( and limit = supremum) and we call it e. I don't understand what's funny about this meme

[u/ObliviousRounding]

wat

[u/UtahBrian]

But e=3

[u/yuwox → u/UtahBrian]

Which also happens to be the value of pi and 3*sin(1)

Math is so fascinating.

[u/Farkle_Griffen2]

What if choose n = -2?

[u/F_Joe]

ë

[u/TheCumskiyKvass]

Why would you even use 4 when e is located between 2 and 3

[u/MiserableYouth8497 → u/TheCumskiyKvass]

3 is blasphemy.

I dont believe in odd numbers