Black Hole Gravity at a Distance

[Sothh]

Here is something I have been wondering for a long time, and just not had time to post yet.

If a black hole has infinite gravity, and you plug infinity into the gravity equation, don't you get infinite gravity no matter the distance?

I know there is something I am missing, but I thought it was an interesting question.

 

[Janus]

Black holes don't have infinite gravity. The gravity of a black hole at any given distance is no greater than that of any other object of equal mass at that same distance. For instance, if we were to replace the Sun with a black hole of equal mass, the orbit of the Earth would remain unaffected.