How big are black dwarfs?
Somewhere between
These limits are all caused by gravity: if a white dwarf is larger than the Chandrasekhar limit, its gravity will be too great and lead to the atoms' electrons collapsing; if a star starts at a mass too low for proper fusion to occur, it will eventually become a white dwarf less than half the mass of the sun. These objects do exist, but they are not true stars; they are known as brown dwarfs.
What relationship does a white dwarf's mass have to a black dwarf?
As a white dwarf does not lose mass during the transition from one stage of evolution to the next, a black dwarf's mass would be the same as that of a white dwarf. A black dwarf is the hypothetical result of a star that has evolved to the white dwarf stage and then subsequently radiated all of its heat energy away, so that it is the temperature of the space background (about 2-3 degrees K).
Since it is estimated to take a trillion years for the coolest known white dwarf to radiate all of its remaining heat, it will be some time before we can determine whether white dwarfs genuinely evolve into black dwarfs.
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As the last stage of a white dwarf star's evolutionary cycle, black dwarfs are hypothetical objects that have not yet been observed. They are thought to be roughly the size of Earth and have a mass similar to that of the Sun, but because of their extremely low temperatures, they would be very faint and challenging to directly detect.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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