Transcendental numbers

Question

Can transcendental numbers be plotted? Also, can a computer recognize a transcendental number? I mean, for example, a computer, while computing, understand that the number it is computing is not exactly $\pi$, but will stop hundred places after the decimal point? If so, how?

Answer 1

I don't understand the “plotted” part. However, I can tell you that computers cannot recognise transcendental numbers if what is meant is this:

Suppose that we have an algorithm that generates a sequence $a_0,a_1,a_2,\ldots$ of digits. Can we determine if, yes or no, the real number$$a_0.a_1a_2a_3a_4$$is transcendental?

There is no algorithm for that because, if there was, it would have been applied to determine whether or not, say, the Euler–Mascheroni constant is transcendental. We don't even know whether it is rational or not! And the computers are programmed with algorithms developed by human beings.

Answer 2

No, the first digits of a number do not allow you to predict the following ones. No way. You need extra information that explains how the number was defined.

And as you know, computers are very poor at thinking.

But try this link, you will be amazed (click Standard Lookup and enter a number): https://isc.carma.newcastle.edu.au

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The accuracy of any "plotter" is limited to 3 or 4 significant digits so that even rationals and irrationals make no difference: any extra digit you provide will be truncated.