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- Irrational + irrational = rational - Physics Forums
Assume 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
- Irrational number to an irrational power - Physics Forums
But as for the original question, this is a well-known proof that's often cited as a classic non-constructive proof The proposition is that an irrational raised to an irrational power can be rational So we consider ##x = \sqrt{2}^\sqrt{2}## Either ##x## is rational or irrational If it's the former, our work is done
- Factoring irrational equations - Physics Forums
However, if "0" does not appear, then the number in the brackets is not a value of x, so you must choose from the list of numbers (the ±1, ±5 3, ±1 3, ±5) However, after going through every possible number in that list, none ever got to "0" which means that the equation does not have any rational numbers (so the answer must be irrational)
- Irrational Numbers and Real Life I need 6 answers - Physics Forums
Irrational numbers are useful within mathematics only, but for that exact reason they are useful in the real world They allow us to develop theories with useful concepts like derivatives, integrals, the various results of analytical geometry, the rules trigonometry etc
- Constructing Lengths with Irrational Numbers - Physics Forums
By the way, abstract mathematics is inconsistent in that they treat irrational numbers as being both, infinite decimal expansions, and precise calculus limits In other words, Cantor's famous diagonal proof that the set of real numbers has a larger cardinality than the set of natural numbers depends on the infinite expansion of decimal numbers
- Can one use an irrational number as a base? - Physics Forums
All numbers, including integers, rational numbers, and irrational numbers, are defined independently of any numeration system I kind of get that, but I am missing what a rational number is, I think If I take and lay straight a rope of unit length in the base 1 number line, I can then cut a rope that is the length of the circle enclosing the
- Proving Root n is Irrational: Perfect Square Affects Proof - Physics Forums
n divides q^2, therefore n divides q Now n is a common factor for p q But we know that p q are co-prime Hence our assumption is wrong, root n is irrational 2) if n is a composite Let's say it is product of two primes c1 c2 The proof remains the same for any number of primes
- Square Root of an Irrational Number is Irrational - Physics Forums
By contraposition, if a is irrational then √a is irrational QED There's no need to look at the inverse of "if a is irrational then √a is irrational" and find a contradiction because the two statements "if √a is rational then a is rational" and "if a is irrational then √a is irrational" are one and the same, just worded differently
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