Let us go back to "cold" hard logic."Time"

[Mystic]

It does follow from the argument I used for it that an infinite line would span infinitely both ways. There would be no end on either end.

Bi-directionality isn't a requirement of an infinite line.  It can start at my nose and extend unto infinity and be an infinite line. 

True in mathematical potentials, but actually infinite line cannot have a start. I cannot be limited. That is the definition of infinity is unlimited.

Either time is limited or not. If it is unlimited it cannot be contained in finite space so let alone start from your nose.