### Some articles on *numbers, number, algebraic numbers, algebraic*:

Cantor's First Uncountability Proof - Is Cantor's Proof of The Existence of Transcendentals Constructive or Non-constructive?

... proof of the existence of transcendental

... proof of the existence of transcendental

**numbers**is constructive—that is, it provides a method of constructing a transcendental**number**... is not "constructive," and so does not yield a tangible transcendental**number**... If we set up a definite listing of all**algebraic numbers**… and then apply the diagonal procedure …, we get a perfectly definite transcendental**number**(it could be computed to any ...Strong Four Exponentials Conjecture

... of this conjecture deals with the vector space over the

... of this conjecture deals with the vector space over the

**algebraic numbers**generated by 1 and all logarithms of non-zero**algebraic numbers**, denoted here as L∗ ... So L∗ is the set of all complex**numbers**of the form for some n ≥ 0, where all the βi and αi are**algebraic**and every branch of the logarithm is considered ... x1, x2, and y1, y2 be two pairs of complex**numbers**with each pair being linearly independent over the**algebraic numbers**, then at least one of the four**numbers**xi ...Irrational Number - Transcendental and Algebraic Irrationals

... Almost all irrational

... Almost all irrational

**numbers**are transcendental and all real transcendental**numbers**are irrational (there are also complex transcendental**numbers**) the article on transcendental**numbers**... Another way to construct irrational**numbers**is as irrational**algebraic numbers**, i.e ... Suppose you know that there exists some real**number**x with p(x) = 0 (for instance if n is odd and an is non-zero, then because of the intermediate value theorem) ...Lindemann–Weierstrass Theorem

... very useful in establishing the transcendence of

... very useful in establishing the transcendence of

**numbers**... αn are**algebraic numbers**which are linearly independent over the rational**numbers**Q, then eα1.. ... αn are distinct**algebraic numbers**, then the exponentials eα1.. ...Transcendental Number - Properties

... The set of transcendental

... The set of transcendental

**numbers**is uncountably infinite ... are countable, and since each such polynomial has a finite**number**of zeroes, the**algebraic numbers**must also be countable ... But Cantor's diagonal argument proves that the real**numbers**(and therefore also the complex**numbers**) are uncountable so the set of all transcendental**numbers**must also be ...### Famous quotes containing the words numbers and/or algebraic:

“Out of the darkness where Philomela sat,

Her fairy *numbers* issued. What then ailed me?

My ears are called capacious but they failed me,

Her classics registered a little flat!

I rose, and venomously spat.”

—John Crowe Ransom (1888–1974)

“I have no scheme about it,—no designs on men at all; and, if I had, my mode would be to tempt them with the fruit, and not with the manure. To what end do I lead a simple life at all, pray? That I may teach others to simplify their lives?—and so all our lives be simplified merely, like an *algebraic* formula? Or not, rather, that I may make use of the ground I have cleared, to live more worthily and profitably?”

—Henry David Thoreau (1817–1862)

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