Timeline for How to find irrational numbers between rationals. (And is my method correct?)
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 25, 2016 at 21:47 | comment | added | Peter S | @Vlad Thanks. Yes that shows how it works. | |
| Jan 24, 2016 at 22:47 | comment | added | Ataulfo | @Vlad: this does not work if the product $ab$ is a square. | |
| Jan 24, 2016 at 22:16 | comment | added | r12 | This post does not demonstrate a way to find irrational numbers between a given set of numbers. It shows a way to find one irrational number between one pair of numbers. | |
| Jan 24, 2016 at 18:49 | comment | added | Peter S | @CuddlyCuttlefish In that case, it would be better using another method. Instead of a method that "may" work and then needs more checking. | |
| Jan 24, 2016 at 18:45 | comment | added | user208649 | It works in this case, and it might work other times, but you will have to justify that it is irrational. | |
| Jan 24, 2016 at 18:31 | comment | added | Peter S | @CuddlyCuttlefish So then, this method does not work? | |
| Jan 24, 2016 at 18:17 | comment | added | user208649 | $\sqrt{2/1\times 8/1} = 4$, and you have neither $2$ nor $8$ perfect squares. | |
| Jan 24, 2016 at 17:43 | comment | added | Peter S | @Ramchandra Apte That's interesting. Does this mean that the method does not work? Or is it because 1 is special and, because of this, an exception? Perhaps 1 also counts as an irrational number (I don't know why, but 1 has strange properties in mathematics). | |
| Jan 24, 2016 at 17:30 | comment | added | Ramchandra Apte | This doesn't always work. $\sqrt{3/2*2/3} = 1$. | |
| Jan 24, 2016 at 16:28 | comment | added | Peter S | (Excuse me, I made a mistake before I edited my previous comment/reply. I wrote "fraction" when I should have written "multiple". I've corrected it now.) | |
| Jan 24, 2016 at 16:25 | comment | added | Peter S | I believe √(ab) is irrational because a is a non-perfect square number. And non-perfect square numbers are automatically irrational (they do not have rational square roots). And so a multiple of an irrational numerator is an irrational fraction/number. However, I had to learn all this in about a day, so I'm also interested in how we know (is there a formula?) a number is irrational or not. | |
| Jan 24, 2016 at 16:20 | comment | added | Vlad | Could you please elaborate more on why sqrt(ab) is irrational (in the general case)? | |
| Jan 24, 2016 at 16:18 | comment | added | Peter S | Thanks for the reply. This is an interesting method too. I more or less understand, but it'll become clearer in the next few days. I'm going to think about this too. It's all a bit clearer now. | |
| Jan 24, 2016 at 16:03 | history | answered | Ataulfo | CC BY-SA 3.0 |