Infinity and Distance

Bored one day, long ago, I was thinking about some of the strange constants of the universe, like infinity (which I spent about 5 hours trying to round off) the speed of light as the theoretical constant of absolute speed... that sort of thing. I had my own theory.

Here it is: You are traveling to a point that is an infinite distance away and are traveling at a speed that is infinitely fast.
How long would it take you to get there?

How far would you have moved after any period of time?

By definition, infinity can never be reached. Therefore, you would always be the same distance away. Because of the afore mentioned definition, you would always be the same distance away and will never really have moved at all. (All of this is relative, of course).

None of this is true. Maybe. Hey, I never said it was original or exciting, just a theory. It's your fault, really; no one made you look in here. It's not like I MADE you look at this crap, did I? No, I didn't. That's right, buck-o, you looked in here yourself and have no one else to blame.

All horses are the same color:
The argument:
The argument is proof by induction. First we establish a base case for one horse (n=1). We then prove that if n horses have the same color, then n+1 horses must also have the same color.

Base case: One horse
The case with just one horse is trivial. If there is only one horse in the "group", then clearly all horses in that group have the same color.

Inductive step:
Assume that n horses always are the same color. Let us consider a group consisting of n=1 horses.

First, exclude the last horse and look only at the first n horses; all these are the same color since n horses always are the same color. Likewise, exclude the first horse and look only at the last n horses. These too, must also be of the same color. Therefore, the first horse in the group is of the same color as the horses in the middle, who in turn are of the same color as the last horse. Hence the first horse, middle horses, and last horse are all of the same color, and we have proven that:

If n horses have the same color, then n=1 horses will also have the same color.

We already saw in the base case that the rule ("all horses have the same color") was valid for n=1. The inductive step showed that since the rule is valid for n=1, it must also be valid for n=2, which in turn implies that the rule is valid for n=3 and so on.

Thus in any group of horses, all horses must be the same color.

Every Horse has an Infinite Number of Legs (Proof by Intimidation):
1. Horses have an even number of legs.
Behind they have two legs, and in front they have fore legs. This makes six legs, which is certainly an odd number of legs for a horse.
But the only number that is both even and odd is infinity.

2. Therefore, horses have an infinite number of legs.

3. Now to show this for the general case, suppose that somewhere, there is a horse that has a finite number of legs. But that is a horse of another color, and by the [above] lemma(*) ["All horses are the same color"]; therefore, that horse does not exist.

(*) A lemma is an auxiliary proposition used in the demonstration of another proposition.

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