anybody having good knowledge of maths, please answer this question? please read details.?

Question

we are taught that parallel lines meet at infinity. please tell that how lines can be parallel and still meet at infinity? if you say they tend to meet at infinity, it is also not correct because parallel lines means they have to maintain equal distance throughout, how they can bend at any point and tend to meet at infinity. draw parallel lines on a page and use all ur logic, maths skills etc. u cannot say infinity is absurd because base of calculus such as limit, continuity and differentiation is based on it.u are free to answer any maths scholars, professors and answer this question. don't u think maths is not hundred percent perfect.

Answer 1

The answer to the question depends on exactly what kind of geometry you are dealing with and what "points" and "lines" mean.

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.

Answer 2

Two parallel lines can never meet in applied geometry,

But when dealing with theoritical mathematics :

If the equations of the two lines are :

a x + b y = c

a x + b y = d where c dosent equal d

and get the point of intersetion using determinantes we get :

x = b(d-c)/( ab - ab) = b(d-c)/zero which is an imaginary number called infinty,

So for the value of y will be infinty

So the two palallel lines theoriticay interset at infinity which is a non real statment

Answer 3

Eucldiean geometry :parallel lines do not meet

non-Euclidean geometry: "parallel" lines meet

It's like different religions. Whatever gets you to a reasonable conclusion, works.

Answer 4

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Answer 5

Infinity isn't a place or a point, it's more like a concept.