From eb2c8cc7add6141ca9492daa2a2a8dd6c4a2d705 Mon Sep 17 00:00:00 2001 From: Will Binns Date: Thu, 16 Jul 2020 18:12:16 +0200 Subject: [PATCH] ch04: Fix subscript Resolves #679 --- ch04.asciidoc | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/ch04.asciidoc b/ch04.asciidoc index 24e7d2f4..844b88c2 100644 --- a/ch04.asciidoc +++ b/ch04.asciidoc @@ -186,7 +186,7 @@ There are a couple of special cases that explain the need for the "point at infi If P~1~ and P~2~ are the same point, the line "between" P~1~ and P~2~ should extend to be the tangent on the curve at this point P~1~. This tangent will intersect the curve in exactly one new point. You can use techniques from calculus to determine the slope of the tangent line. These techniques curiously work, even though we are restricting our interest to points on the curve with two integer coordinates! -In some cases (i.e., if P~1~ and P~2~ have the same x values but different y values), the tangent line will be exactly vertical, in which case P3 = "point at infinity." +In some cases (i.e., if P~1~ and P~2~ have the same x values but different y values), the tangent line will be exactly vertical, in which case P~3~ = "point at infinity." If P~1~ is the "point at infinity," then P~1~ + P~2~ = P~2~. Similarly, if P~2~ is the point at infinity, then P~1~ + P~2~ = P~1~. This shows how the point at infinity plays the role of zero.