Does a horizontal line have horizontal asymptotes?

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A horizontal line, such as y = 7, does not have horizontal asymptotes because asymptotes are defined as lines that a function approaches but never reaches. The discussion highlights that while some functions may cross their asymptotes infinitely, a constant function like y = 7 does not fit this criterion. The formal definition of an asymptote involves a curve approaching a line as it tends to infinity, which does not apply to horizontal lines. The topic remains somewhat ambiguous, with arguments possible on both sides regarding the existence of asymptotes for horizontal lines. Ultimately, the consensus leans towards the idea that horizontal lines do not possess asymptotes.
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For example, y = 7. Are there an infinite number of asymptotes at any y value that isn't 7? If so, how would I format this statement on my homework?

*edit* oops sorry, I meant to post this in homework help
 
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I don't think so.

Asymptotes are usually defined as lines that a given function approaches infinitely close, but never reaches. Under this definition, a line has no asymptotes.
 
Vorde said:
Asymptotes are usually defined as lines that a given function approaches infinitely close, but never reaches.

Except functions like ##\frac{\sin x}{x}## cross their asymptote an infinite number of times.

Formal definition from Wikipedia:
Let ##A:(a,b)\rightarrow\mathbb{R}^2## be a parametric curve, in coordinates ##A(t)=(x(t),y(t))##. Suppose the curve tends to infinity, that is:
##\lim_{t\rightarrow b}(x^2(t)+y^2(t))=\infty##.
A line ##\mathcal{l}## is an asymptote of A if the distance from A(t) to ##\mathcal{l}## tends to zero as ##t\rightarrow b##

This is really iffy. You could argue either way.
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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