Guv,

Consider for a moment the gometry of things on the surface of a sphere, Radius R, and draw 2 parrallel lines on it, These of course meet at 2 points on the surface of the sphere, these points are pi*R apart.

Now, making R bigger and bigger 2 things happen, 1, the distance between the lines gets larger, and 2 the surface of the shere becomes flatter.

This leads to the conclusion that plane geometry is in fact the limit of spherical geometry as R tends to infinity.

and so the lines meet at pi*R/2 (which is infinite) in either direction.



The other argument I can think of is if you imagine drawing a line perpendicular to one of the lines, (draw a line d perpendicular to line a, call the other parralell line b)

now, forget for a minute that a and b are parralell, call the angle line d makes with line b theta

So the distance between the points wherea crosses d and where a crosses b is (the distance between the points wherea crosses d and where b crosses d ) * Tan(theta)

and when the lines are parrallel theta = pi/2 and this distance = infinity.



I think the big problem here is a question of how to pronounce the term = infinity.

In maths we don't write the word infinity, we use the drunken eight symbol. So it may not be correct to write the word infinity, as maths symbols do not as a rule correspond exactly to English words, if they did we wouldn't need them.

OK, revert back to your various childhoods for a moment and picture yourself in front of the class reciting your times tables. In my classroom there was a mirror on the wall in front and the times tables written out behind me on big posters. So if you stood in the right place and could read mirror writing you could just read them off the posters.

So picture the scene, in the mirror I can see this

1 x 7 = 7
2 x 7 = 14
3 x 7 = 21
4 x 7 = 28
and all I had to say was

One times seven is seven.
Two times seven is fourteen.
Three times seven is twenty-one.
Four times seven is twenty-eight.
There is a difference between what I was saying and what I was reading. Because I was translating between the written symbols on the posters, and the spoken word the teacher wanted to hear.

Now I wasn't wrong (except morally) A translation had to be made and, as I was 6 at the time nobody was fussed that I was saying is instead of equals.

So after this touching tale of scandal and deciet let's look again at the statement 1/0 = drunken-eight.

maybe rather than pronounceing this as "One divided by zero equals infinity" we can say "One divided by zero is infinite." which is literally "One divided by zero is not finite."

That seems a less controversial meaning to the phrase, esspecially when equality vey much implies the Idea that

a = c & b = c => a = b

wheras it would be very wrong to say

1/0 = drunken-eight
ln(0) = drunken-eight

=> l/0 = ln(0)


So I'd say that "1/0 = drunken eight" is a correct statement as long as it's pronounced correctly, and a misprocunciation is a forgivable mistake, even in maths.