A black hole has an infinite density; since its volume is zero, it is compressed to the very limit. So it also has infinite gravity, and sucks anything which is near it! Not everything there is!! Now above all when it sucks things it adds up to its mass, which remains finite and it always will, even if it did suck in the whole universe!! It's all for the formula: density in a black hole is mass divided by volume (0) so the density is infinite, not the mass!!! So thus a black hole has mass which is finite and will always be finite.
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