The negation of countable. If a set is uncountable, it does NOT have a one-to-one correspondence to the natural numbers.

Check this out:
Real Numbers are Uncountable - proof

Forty seven bricks on the way to work. Twenty seven stairs. About four thousand nine hundred forty two synthetic fiber clusters along a line on the carpet traced down the center of the hallway. One million three hundred ten thousand seven hundred twenty pixels. If only I had a photometer handy.
It is bold to say that we are arriving at a discrete world. But more every day we are being put into one-to-one correspondence with the natural numbers. Sure, it started innocently. An ISBN seems mostly harmless. A loose phone number is usually just a nuisance. How do you feel about your zip code? National Insurance number, Tax File number, INSEE code, Social Insurance number, Social Security number, PPS number, or NIE number? Apple's new iPhone has built-in GPS.

At least no matter how much we quantify and are quantified, technology leaves messy trails. Just look at SMTP, the protocol for e-mail, and HTTP, the protocol behind the world wide web. They are human-readable, designed to be hand-typed, back in the early days of what is now the burgeoning God Internet. Nowadays it's just machines talking to each other. For them, the numbers have no meaning. All they know is cold 0x48454C4F and the furious passion of bits following every GET. One utters to another, 354 Enter mail, end with "." on a line by itself, and promptly everything but 354 is discarded as irrelevant.

We can throw off our shackles. There is hope. I learned about it in math class.

We must become real numbers. We must win by overload, camouflaged within an infinite number of digits, an infinite amount of information. We can show them fear in a handful of sevens. There will be no more zero, or twelve, or three. They will have to invent new number systems because our very skin will ripple with a million reals, and decimals will stream from our eyes, and there will be no world left for counting.


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