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

Strong Four Exponentials Conjecture

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

... The statement 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 ... 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 yj for 1 ...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 ... 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) ...Cantor's First Uncountability Proof - Is Cantor's Proof of The Existence of Transcendentals Constructive or Non-constructive?

... Some mathematicians claim that Cantor's proof of the existence of transcendental

... Some mathematicians claim that Cantor's proof of the existence of transcendental

**numbers**is constructive—that is, it provides a method of constructing a ... proof 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 ...Lindemann–Weierstrass Theorem

... useful in establishing the transcendence of

... 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 ... and since each such polynomial has a finite**number**of zeroes, the**algebraic numbers**must also be countable ... 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 uncountable ...### Famous quotes containing the words numbers and/or algebraic:

“Our religion vulgarly stands on *numbers* of believers. Whenever the appeal is made—no matter how indirectly—to *numbers*, proclamation is then and there made, that religion is not. He that finds God a sweet, enveloping presence, who shall dare to come in?”

—Ralph Waldo Emerson (1803–1882)

“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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