I guess the question the force of gravity in a small black hole is infinite, I would think that there would be no such thing as a large black hole.
Why not? Size by itself has nothing to do with density, as I attempted to exemplify with the Saturn-Earth comparison.
How do you have greater than infinite.
How many numbers are there between 0 and 1? Infinite. There's 0.1, 0.01, 0.001, and so on. Now how many numbers are there between 0 and 2? Also infinite, yet twice
as many as between 0 and 1.
There are many types of infinity. Infinite types, actually. Regardless, adding mass doesn't mean something will become denser.
Adding mass to a black hole to increase the already infinite pull of gravity would appear to be impossible. Shouldn't this make all black holes effectively the same size? Every time I have heard of super massive black holes it seems as if they are described to be different from ordinary black holes.
From my understanding, super massive black holes are named such because they're "super massive"; as in: bigger than "regular" black holes. Their density may or may not be higher. Think of something like wood. Wood floats, correct? It doesn't matter if you have one kilo of wood or one billion kilos; wood will always float because it is less dense
than water. Likewise, you could pump an air bubble equal to the mass of Jupiter into our oceans (if it were possible), and all the air would still burst out of the water, due to its density.
D = M/V.
For D to be infinite, V would be an infinitely small number (or zero, correct?)
How can something have mass but take up zero volume?
Therein lies the problem with infinities in physics (or any branch of anything, really, that doesn't use infinity conceptually). Such a thing is not possible.