No, we don't count from 0. That's like saying we start counting a baker's cup from 0 because you can have half a cup.
Suppose your job is to count some events. You check in for work at 8:00 a.m., but the first event has not registered until noon. By your logic you should not be paid for four hours, because you're paid to count, and counting started at 1.
Your pedometer?
Your traffic clicker?
We are talking about the he numbering, not the work-doing.
You start waiting at 8, and you wait between events. But you only count (increment) when an event happens.
The 0 comes for free when you are ready to count (hello golang and C++, as well as human intuition).
When you count stars in the sky you don't say "0, 1, 2".
You say "..., 1, 2", or if no stars show up, you say "there are 0" after timer expires.
Increment what?
> When you count stars in the sky you don't say "0, 1, 2".
No, you say, "I'm going to start counting stars now. Okay, 1, 2, ...".
The preparation part is the zero. You counted stars before and reached some number; you're not starting at that number.
If you just look at an empty space, the # of apples is equivalent is equivalent to the # of dinosaurs, but they're only equivalent by their absence.
Is the empty set countable? (Yes.)
Dictionary:
nat·u·ral num·bers
the positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well
Set theory:
> Equivalently, a set S is countable if there exists an injective function f : S → N from S to N; it simply means that every element in S corresponds to a different element in N.
Defining N is usually done via a successor set, on which case 0 makes no sense to include.
Standard construction of ordinals is that each ordinal is the set of all its predecessors. (0 has no predecessors , hence 0 is the empty set.) (And so finite ordinals have the same ordinaliity as cardinality).
Birthdays are clearly 1 indexed, the first birthday is indexed with 1, and not with 0.
Birthday[0] gives you an out of range exception, since there is no birthday called 0th. Birthdays are [first,second,..] indexed from 1: brithday[1] = first, birthday[2] = second, and so on. That's what indexing a series from 1 means.
You can't possibly be serious.
I then put it in an initially empty bowl
The milliliters in a baker's cup are a scale based on 0!