Fractus

I still maintain that irrationals (numbers) are aptly named; because they are irrational. An irrational number is an approximation, not an actual value. Numbers are value statements, and so saying that “0.3… is an irrational number” is a misnomer.

1/3 is not 0.3…, even though your calculator will tell you it is. It is not because standard decimal notation has a huge flaw – it is actually forcing representing fractions as a fraction of 10. 3 goes into 10, 3 times, and 1 tenth remains. 3 times 1/10 = 0.3. 0.3 goes into 1, 3 times, and 1 hundredth remains. Ad infinitum – ie infinite regress of the decimal expression. Your math teacher might teach you that this means that 1/3 = 0.3… It is a blatant lie. The result indicates that the decimal system, being confined to base 10, is flawed.

“Fraction” is derived from the latin “fractus”, meaning ‘broken’. The standard decimal system is broken.

A Preview of Farve Abstraction Developer

Hello.

This weekend I started work on the UX (User Experience) for Farve Abstraction Developer. I will share some screenshots. It does not look like much yet, but it will soon.

Curry’s Paradox – What Paradox?

A natural language version of Curry’s paradox might be the following sentence:

If this sentence is true, then Santa Claus exists.

We need not believe, beforehand, that the sentence is true or that Santa Claus exists. But we can ask, hypothetically, if the sentence is true, then does Santa Claus exist?

If the sentence is true, then what it says is true, namely that if the sentence is true, then Santa Claus exists. Therefore the answer to the hypothetical question must be yes: Santa Claus does exist if the sentence is true. However, that is exactly what the sentence states: not that Santa Claus exists, but that he exists if the sentence is true, which is just the hypothetical answer just established. Therefore the sentence is true after all, and since we have established that Santa Claus exists if the sentence is true, and that it is true, it follows that Santa Claus must exist.

Since it is evident that any claim could be “proven” in this manner, there is a paradox.

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According to Wikipedia, this is an unresolved paradox, since there are no consent among thinkers as to its resolution.  Am I mistaken, or does it not logically follow from “However, that is exactly what the sentence states: not that Santa Claus exists, but that he exists if the sentence is true, which is just the hypothetical answer just established.” to “Therefore the sentence is true after all”?  Nowhere were there established that the sentence is true!  It was just established that, if the sentence is true, then the sentence is true.