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Bookmark or Share- Proving Irrationals Are Dense in the Reals - Physics ForumsSome previous results that I'm using is that a rational plus an irrational is irrational, and that a rational multiplied by an irrational is also irrational. So since I knew that for any r that is an element of Q, and x, y that are elements of R, then x
- Showing that tan(1) is irrational - Physics ForumsAn irrational number is a real number that cannot be expressed as a ratio of two integers. In other words, it cannot be written in the form a/b where a and b are integers. How do you prove that a number is irrational? To prove that a number is irrational, you must show that it cannot be written as a ratio of two integers.
- Natural constants: are they irrational numbers? - Physics ForumsA natural constant is considered irrational if it cannot be expressed as a ratio of two integers. This means that the decimal representation of the constant is non-terminating and non-repeating. For example, the value of pi (π) is an irrational number because it cannot be expressed as a fraction. Why are some natural constants irrational?
- Irrational + irrational = rational - Physics ForumsAssume that the difference between a rational number and an irrational number is an irrational number. The sum of any such two irrational numbers would be a rational number. All we have to do now is prove the assumption, which I think is easier. edit: I just saw tongos' proposition, which I think is better than mine.
- Prove the Irrationality of the Golden Ratio & Phi - Physics ForumsWhy is the Golden Ratio considered irrational? The Golden Ratio is considered irrational because it cannot be expressed as a fraction of two integers. It is a non-repeating, non-terminating decimal and its digits go on infinitely without forming a pattern. What is the proof of the irrationality of the Golden Ratio?
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