The equality of x^n/x^m and x^(n-m)

[Indistinguishable]

Er, I’ve swapped some ms and ns above. You all know what I mean.

[j_sum1]

mn

[Senegoid]

@The_Lurker_Above

[Mathematician Trolling] Yeah, you’d think the fact that our bridges (mostly) don’t fall down would be proof enough that the technique works! [/MT]

[Trolling Back Atcha] It only takes one counterexample! [/TBA]

(And in my Diff Eq textbook, there was a sidebar about a bunch of airplanes that did that too. In mid-flight! :eek:)

[Senegoid]

@Thudlow_Boink

So I’ve been looking up the laws of exponents (a[sup]m[/sup]/a[sup]n[/sup] = a[sup]m-n[/sup] et al) in a few Intermediate/College Algebra textbooks I have handy. Most of them include the condition that a is nonzero, or they say something like “where defined” or “assuming denominators are not zero.”

Basically, a[sup]m[/sup]/a[sup]n[/sup] equals a[sup]m-n[/sup] (except when it doesn’t). Seems to cover all the bases.

[leahcim]

@Senegoid

[Trolling Back Atcha] It only takes one counterexample! [/TBA]

(And in my Diff Eq textbook, there was a sidebar about a bunch of airplanes that did that too. In mid-flight! :eek:)

Indeed, the fact that bridges don’t fall down has more to do with the safety factors built into bridge designs than the validity of engineer’s mathematical methods. Build to carry twice the maximum expected load and it doesn’t matter that your calculation of how much load the bridge can carry is off by 5% due to some not-quite-justified mathematical jiggery-pokery.

[Chronos]

“Off by 5%” is a different sort of mathematical jiggery-pokery than what’s being discussed here. Removable discontinuities don’t give you results that are off by a little bit: Depending on your perspective, they either give you results that are exactly right, or results that are off by “What the Hell are you talking about!??!”.

[Thudlow_Boink]

@Chronos

“Off by 5%” is a different sort of mathematical jiggery-pokery than what’s being discussed here. Removable discontinuities don’t give you results that are off by a little bit: Depending on your perspective, they either give you results that are exactly right, or results that are off by “What the Hell are you talking about!??!”.

I can find plenty of examples online—like this or this or this

(though, to be fair, those look more like nonremovable discontinuities)

[Learjeff]

@Senegoid

@Asympotically fat

I deeply resent the idea that I know what I’m talking about!

I myself only just noticed the correct spelling of your name rather recently. :smack:

And I never noticed the missing T in in Asympotically fat’s handle! :smack:

[Senegoid]

@Thudlow_Boink

I can find plenty of examples online—like this or this or this

(though, to be fair, those look more like nonremovable discontinuities)

Anybody recognize where that third picture (this one) is taken? Is it at Lake Berryessa, Ca.? That’s where it looks like to me. (Although I don’t know for sure if the mountain in the background is right.) Are there other places that look like that?