Q: Why do rational rules result in a double-bind?

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Any integer can be divided by any non-zero integer, and the result is a rational number.

The result will also be a rational number.

Not necessarily. The value of 3 (rational) raised to the power 1/2 (rational) is not rational.

It is irrational - unless the divisor is 0 in which case the division is not defined.

If you multiply a rational and an irrational number, the result will be irrational.

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Any integer can be divided by any non-zero integer, and the result is a rational number.

Wats are temples from South East Asia and, as far as I am aware, they do not dicatate any rules for adding rational numbers.

The rules are the same.

When the rational number is 0.

The result will also be a rational number.

Not necessarily. The value of 3 (rational) raised to the power 1/2 (rational) is not rational.

It the combination is multiplication and the rational number is 0, then the result is rational. Otherwise it is irrational.

It is irrational - unless the divisor is 0 in which case the division is not defined.

If you multiply a rational and an irrational number, the result will be irrational.

Unless the rational number is zero, the answer is irrational.

Any addition, subtraction, multiplication, or division of rational numbers gives you a rational result. You can consider 8 over 9 as the division of 8 by 9, so the result is rational.

If an irrational number is added to, (or multiplied by) a rational number, the result will always be an irrational number.