If I wanted a word that indicated the absence of a property, like how 'inorganic' means 'not containing carbon,' what prefix might I use to indicate that?
Mono- "one" and poly- "many" are Greek prefixes. The Greek prefix a- (normal form) or an- (before vowel or h) means "not", and it can also indicate the absence of something. That is why it is often called the alpha privans, the "depriving a". Wikipaedia:
An alpha privative or, rarely,privative a (from Latin alpha prīvātīvum, from Ancient Greek α στερητικόν) is the prefix a- or an- (before vowels) that is used in Greek and in English words borrowed from Greek to express negation or absence, for example atypical, anesthetic, and analgesic.
Cf. atypical "not being of a type", atopical "not at a specific place", amorphous "without form", anaemic ("lacking [red] blood [cells]").
Chemists use de or des.
Desoxymescalne, or deoxyuracil etc.
If you are asking for a productive prefix that can be used in the same way "mono-" and "poly-" are, I do not think one exists. For example, there are such things as "monogamy" and "polygamy", but no prefix attachable to "-gamy" gives the meaning not marrying. Same thing with monoplane, polyunsaturated, monofocal, etc.
If you just mean a prefix that can be used to mean absence, then "a-", "an-", "de-", "in-", "non-", "un-" are all used in different cases. For example, ocean water devoid of oxygen due to eutrophication might be described as "anoxic", while the blood running through your veins back towards your heart might be described as "deoxygenated" or "unoxygenated". There doesn't seem to be any one term that can be used in every case.
Mono- and poly- are Greek prefixes.
A- an- and ag- are all negatives in Greek. But I don't think a negative is what is wanted (see comments).
I think we want to say 'without'. I don't think we want to say 'not'.
The Greek for 'not even one' is ουδεις, oudeis.
But 'oido' is a more English pronunciation.
- polychromatic, a painting with a variety of colours
- monochromatic, a painting with only one hue
- oidochromatic, a painting without colour, that is, in greyscale.
[Black and white are not, technically, colours and should not be referred to as 'monochrome'.]
Then we drop the second 'o' and use 'oid -' as a prefix for vowels.
[Polygamy, monogamy and oidogamy would thus be the sequence referred to above.]
It's easy to remember because its first letter is reminiscent of a zero.
'In' seems to be a bit of a problem (see comments, again).
'Inflammable' means 'highly flammable'. It doesn't mean 'not flammable'. 'Inestimable' means 'beyond estimation'. It doesn't mean 'there is nothing there to be estimated'. 'Incalculable' means 'infinite'. It doesn't mean 'there is so little there that you cannot calculate it'.
'Inorganic' should mean 'it's so organic, you just wouldn't believe it.'