csprof2000 said:
To be fair, you pretended you knew what *I* was saying when I said what I did
One of the most basic semantic conventions is that when a particular word has an established usage, that anyone using that word unqualified means that usage.
I never made any representation that I believed in your version of reality
Reality?
What does that have to do with anything?
Plus, given the definition I provided from a (possibly less than reputable) third party, it seems a fair enough issue to give me the benefit of the doubt.
General purpose dictionaries good for defining words in every day usage. They're notoriously bad at defining technical words. (After all, their purpose is the former, not the latter)
How would you define "finite", exactly?
Depends on the context. When dealing with sets with an ordering and contain integers, by far the most typical definition is:
x is finite if and ony if it lies between two integers
or something equivalent; for example, I would be entirely unsurprised to see a textbook define a finite extended real number simply by "it's neither +\infty nor -\infty".
When dealing with sets, the typical definition is
S is finite if and only if there is a 1-1 correspondence between S and a bounded interval [0, n) of natural numbers, for some natural number n
(Or something obviously equivalent) (Note that [0,0) has a 1-1 correspondence to the empty set)
And for
cardinal numbers,
A cardinal number x is finite if and only if it is the cardinality of a finite set
Or, sometimes, I've simply seen it defined by the equivalent statement that a cardinal number is finite if and only if it's a natural number.
Zero is certainly a peculiar finite number, if you consider it to be such. No sign, no multiplicative inverse,
Every number has its own pecularities.
and semantically meaning the absence of quantity.
Nononono. First off, it can only possibly have any relation to the idea of quantity in the particular case we are using a number to quantify something. Quantification is not inherent to the mathematical notion of number.
Secondly, a quantity of zero is not the "absence of quantity". After all, if the quantity is zero, then there is certainly a quantity involved.
"The number of coins in my pocket" is a quantity, and that quantity can be zero.
"Blue" is not a quantity. It would be nonsensical to say "Blue" is zero.
Don't confuse yourself by the fact natural language has evolved to special-case zero.
I would imagine that one could also go off into fantastical reveries (much like has been done with infinity)
What are infinitesimals if not a kind of zero?
Nonzero.
(Actually, zero is an infinitessimal. All other infinitessimals would be nonzero)
Anyway, done with this rant. Jeez, you guys take things so personally sometimes. It's not about trying to say you're suckers for seeing things one way.
You claim to be a CS professor... what if I came into your class and tried to tell you that 1 is not O(x), or that the halting problem was computable? And then when you corrected me, I simply accused you of mindlessly 'parroting conventional wisdom'?