Parallel Lines can meet when you actually apply them in 3D dimensions. The best example I have would be the longitude lines on Earth. They're exact distances apart and parallel, but they do touch at the North and South pole
It's probably because it looks just like an infomercial "Tired of spilling all your sauce everywhere? well, do I have an offer for you! turn it back upward and **** will stop falling out."
Well, technically a tangent like can cross at multiple points. For example in the graph to the right the tangent line passes through the graph twice. A tangent line is not a line that crosses a function once. A better way of explaining it would be to imagine the tangent line crossing the curve at point P would be to define point Q as any other point on the curve. The secant line joining point P and point Q would become the tangent line when Q is brought to and is point P.
So a tangent line could possible cross a line an infinite number of times (An easy example would be either tangent line with slope = 0 on either the sin or the cos functions.)
well its like saying, tell me the biggest number and i'll give you 1 million dollars
will i ever give you a million dollars?
no
even if youll try forever
first because i dont have million dollars, but still you wouldn't get them
No, No they don't. Parallel lines are always the same distance apart and never get any closer. They will never meet even at infinity. You are thinking of an asymptote.
If you are talking about ordinary lines and ordinary geometry, then parallel lines do not meet. For example, the line x=1 and the line x=2 do not meet at any point, since the x coordinate of a point cannot be both 1 and 2 at the same time.
In this context, there is no such thing as "infinity" and parallel lines do not meet.
However, you can construct other forms of geometry, so-called non-Euclidean geometries. For example, you can take the usual points of the plane and attach to them an additional point called "infinity" and consider all lines to also include this additional point. In this context, there is a single "infinity" location where all lines meet. In a geometry like this, all lines intersect at infinity, in addition to any finite point where they might happen to meet.
Or, you could attach not just one additional point, but a whole collection of additional points, one for each direction. Then you can consider two parallel lines to meet at the extra point corresponding to their common direction, whereas two non-parellel lines do not intersect at infinity but intersect only at the usual finite intersection point. This is called projective geometry, and is described in more detail in the answer to another question.
In summary, then: in usual geometry, parallel lines do not meet. There is no such thing as infinity, and it is wrong to say that parallel lines meet at infinity.
However, you can construct other geometric systems, whose "points" include not only the points of familiar geometry (describable as coordinate pairs (x,y)), but also other objects. These other objects can be constructed in various ways, as described in the discussion of projective geometry. In these other geometric systems, parallel lines may meet at a "point at infinity". Whether this is one single point or different points for different classes of parallel lines, depends on the particular geometric system you are considering.
lol, it was a quote from a mathematic site.
it means that there are situations and definitions in wich parallel lines meet in infinity. even though in normal language and the lower mathematics thats not true.
sin(x)/x is continuous isn't it?, it just gets smaller and smaller in its arcs to infinity, but it is constantly continuous, and I think is even differential. On oscillating functions though yeah I don't think they're continuous at x=0, or generally around that.
Haven't come on much lately? Blue eye is spoiler tags, you hover your mouse over it to see the spoiler.
What the problem with that definition who thinks lines are the way reaper said in the first comment, is they'll say "Well aren't points just really small dots?"
So a path is more adequate in explaining it to that first question.
Wikipedia: Trigonometry (from Greek trigōnon "triangle" + metron "measure"[1]) is a branch of mathematics that studies triangles and the relationships between the lengths of their sides and the angles between those sides.