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Can't Think of a Breaking Bad Pun For the Title: Let's Do Some Math!

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Carl-E:
I guess only vertical asymptotes are observant Catholics, then. 

'cause other types can touch, they just usually don't... maybe they're just picky?   :roll:

Loki:
*blink* how exactly does an asymptote touch whatever it is asymptotic to?

Carl-E:
Take a look at y = {sin(x)}/x.  Asymptotic to y = 0 as x -> infinity, and crosses it at every multiple of pi. 

There are rational examples, too, like y = x/(x^2 + 4), which is also asymptotic to y = 0 as x -> infinity, but crosses it at the origin. 

And it's not just the x-axis; any horizontal, slant or curvilinear asymptote can be crossed by a function that it's asymptotic to. 

Just not the vertical ones. 

Loki:
Huh. Yeah, I see now - thanks!

Pilchard123:
Partially related, but useful in other cases too. https://www.desmos.com/calculator

You have dialled an imaginary number. Please rotate your handset by 90 degrees and try again.

(click to show/hide)Zorn's lemon
(click to show/hide)An Abelian grape
(click to show/hide)A non-Abelian grape (click to show/hide)Because it doesn't commute
 :claireface:

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