What makes a number transcendental?

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I read wikipedia about transcendental numbers and I honestly didn’t understand most of what I read, nor why it should be important that e and pi (or any numbers) are transcendental.

In: Mathematics

5 Answers

Anonymous 0 Comments

I may be missing some weird cases, but I read it this way:

Start with integers and *i* and try to create new numbers by addition, multiplication, subtraction, division, and exponents. And no fair doing something an infinite number of times.

You get 0.5 by dividing (1/2). You can get 0.75 by using division and addition ((1/2) + (1/4)). You can get the square root of 2 using division and exponents (2 to the power of (1/2)).

The numbers you can’t get are transcendental. They are hard to find in part because you can’t describe them with normal elementary math operations.     

However, most numbers are difficult to find and use. In fact we can’t even describe most numbers. Most numbers are [uncomputable](https://en.wikipedia.org/wiki/Computable_number).

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