Counting to one is not well defined. Or more precise, "Counting to x" isn't well defined. It basically says iterating until the number one but you don't specify from where, over what elements nor in what order.
We know where dealing with numbers, but what numbers? ℕ, ℤ, ℤ
+, ℚ, ℝ, ℂ (or even ℍ)? Merely saying "count to x" means I can take any path that leads to x in, say, the complex plane (or quaternion space). For example, let's say we have the set A ⊆ ℂ and let A = {-1, 1, 3.14, π, 1+i}. "Count to one" says I can choose any path in A that ends in 1. That could e.g. be 3.14, π, 1+i, -1, 1.
If you specify order, then you can throw out complex numbers and quaternions as they're not an ordered set. What we're left with are the reals and with them you can specify two directions, but you will still have infinite paths. But let's say you go in an increasing order. Great, one direction, but still infinite paths. For the sake of practicality, you limit yourself to the integers, ℤ. Still infinite paths since the lower boundary is not determined yet. For whatever reason, say simplicity or design, the lower boundary is set to 1, implying further restricting us to ℕ. Thus we have a definition on "Count to x":
First, define the well ordered set A = {∀y | ∃x ∧ x,y∈ℕ ∧ 1 ≤ y ≤ x}, ordered in increasing order from left to right. (Example, A = {1, 2, 3, 4, 5, 6} for x = 6)
"Count to x", call it a function C(x), is then defined as iterating through each element in set A from left to right where x is the upper limit as shown in the set's definition with the same restraints.
Now we get to the question. What about C(1). Based on the definition above, you have A = {1}. You iterate through it. What do you get? 1. That's it.
If you still want to argue about "to", how about this compromise:
Every set contains the empty set (including the empty set itself!). Lists are sets, in mathematics, computer science and everyday life. Thus A = {Ø, 1}.
Counting to 1: Ø, 1.
But that's just me.
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Topic: Things that made you go "WTF?" today o_O (Read 14846176 times)