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I'm wondering how transcendental numbers work! I can understand the proofs of irrational numbers.. But I'm not able to understand for transcendental.. Can you explain a simple proof of a transcendental number(any number like pi or e or something)? And How people came to know transcendental numbers exist? Help me please!

Hello Shameem

I'm sorry to say that a simple proof does not exist. Unless you are at least at doctorate level.

Liouville gave the first proof that a transcendental number exists.

If you are familiar with the proof that the rationals are countable, then a similar stacking proof can be used to show that the algebraic numbers are countable, by listing them by the coefficients of their polynomial equation. That leaves an infinite number of uncountable numbers. These are the transcendentals.

So can I refer you to http://en.wikipedia.org/wiki/Transcendental_number.

Best wishes

vijilant

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