In this particular context, 'discrete' means a quantity that's made up
of lumps that can't be split up, like a pound of jellybeans, or an ounce
of sand. If you cut it down to smaller and smaller samples, you eventually
get down to the smallest possible lump ... one jellybean, or one grain of
sand ... and there's no smaller amount of it. That also means that a large
amount of it can only have certain values ... a number of jellybeans, or a
number of grains ... and it can't have values in between.
Electric charge is like that. The smallest possible amount of charge is
the amount that one electron carries. No matter how much or how little
charge you have in your pocket, it can't be the amount of charge on, say,
a million electrons plus half of an electron. It has to be the charge on a
whole number of electrons.
Of course, the charge on an electron is so tiny that we never see how
charge is actually made up of little lumps that can't be split up. To us,
it always looks like you could take as small an amount of charge as you
want ... even as little as, say, 0.1 electron's worth, or even less. It looks
to us as if charge is . . .
'Continuous' ! That just means it's a quantity that's NOT made of little
lumps. You can 'pour' it. You can split it up as fine as you want, and
you'll never find any minimum amount. It's smooth like water, not grainy
like sand.
Of course we know now that even water has minimum amounts ...
molecules ... and if you cut up a molecule of water, then you don't
have water any more. And in fact, even pure elements, like hydrogen,
are discrete. They're made up of atoms, and if you cut up an atom of
hydrogen, then you don't have hydrogen any more ... you have broken
pieces of an atom.
But you get the idea. 'Discrete' means made up of small units that
can't be subdivided. 'Continuous' means smooth, with no minimum
units no matter how close you look at it.
