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/sci/ - Science & Math

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12236460 No.12236460 [Reply] [Original]

How would you mathematically describe a line infinitely close to being horizontal?

Let's say it goes through [0, 0]. Would it at the "ends" still be infinitely close to 0 as [inf, 0+] or [inf, inf]?

I mean it's not like your regular lim of a curve. It's ever so slightly tilted line and should eventually get away from 0.

But even very little tilted line going through [0, 0] and e.g. [g64, 1/g64] could be even less tilted: [g64, 1/(g64*2)].

>> No.12236591

If you described your line as a standar function, it would obviously be [inf, inf] at the end. This is because the function would have to have some non-zero slope which, when multiplied by infinity, becomes infinity

>> No.12236610

>>12236591
Infinity can't be multiplied.

>> No.12236621

>>12236460
y=0

>> No.12236630

>>12236460
If the line goes through [0, 0] and [1, 0.000...1], then it's infinitely close to being horizontal. The line crosses into infinity at [inf, 1].

>> No.12236634

Y= +/-(lim 1)x+b

>> No.12236651

>>12236460
>How would you mathematically describe a line infinitely close to being horizontal?
You wouldn't, as that is not mathematically coherent. There's no such thing as "infinitely close".

>> No.12236653

>>12236591
yeah but it has infinitely small slope 1/inf and lim of that is 0
what's lim of x/inf for x->inf?

>> No.12236852

>>12236460
[math] \lim_{x \to \infty}(\text {any non zero slope})x = \infty [/math]

>> No.12237036

>>12236460
>a line that's infinitely close to horizonal
just set the left end at point (0,0)
and the right end at (x,1/x)
as x approaches infinity, the line connecting the two points becomes infinitely close to horizontal

https://www.desmos.com/calculator/slkjzmm3ly

>> No.12237624

>>12236460

Jesus Christ I thought his leg was off. But now that I realize all that booze was dropped, that's almost as bad.

>> No.12237701

>>12236460
>How would you mathematically describe a line infinitely close to being horizontal?
infinitesimal slope
[eqn]y(x)=\varepsilon x+b[/eqn]
where [math]\frac{1}{x}>\varepsilon\quad\forall x\in\mathbb{R}[/math].

>> No.12237704
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12237704

>>12236460
As long as the distance AB>0, C moves along the bottom horizontal line.
Once AB=0, C is on the top horizontal line, if anywhere.
This is infinity. Infinity is larger than any real number. Infinity isn't a number.

>> No.12237739

>>12236460
unless you allow infinitesimals, you cannot make sense of this

>> No.12237867

>>12236460
>Would it at the "ends" still be infinitely close to 0 as [inf, 0+] or [inf, inf]?
there's no "end" to infinity, retard. and "inf" isn't a coordinate

>> No.12237870

>>12237739
wrong, the question as framed is nonsense even if you do allow infinitesimals

>> No.12237964

>>12236460
All the lines in R^2 that pass through the origin are isomorphic to the 1d circle S^1 (look up projective spaces). Therefore a line "infinitely close" is like saying the largest number in the interval [0, 1) i.e. 0.999... So the answer is probably that it is the horizontal line.