proved that e is irrational; that is, that it cannot be expressed as the quotient of two integers. Euler wrote the first proof of the fact that e is irrational...
11 KB (1,583 words) - 06:28, 5 July 2024
the 1760s, Johann Heinrich Lambert was the first to prove that the number π is irrational, meaning it cannot be expressed as a fraction a / b {\displaystyle...
25 KB (5,785 words) - 22:04, 3 August 2024
In mathematics, the irrational numbers (in- + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed...
39 KB (5,252 words) - 15:03, 28 June 2024
mathematical constant e can be represented in a variety of ways as a real number. Since e is an irrational number (see proof that e is irrational), it cannot be...
11 KB (2,028 words) - 01:55, 12 April 2024
proof Mathematical induction and a proof Proof that 0.999... equals 1 Proof that 22/7 exceeds π Proof that e is irrational Proof that π is irrational...
6 KB (593 words) - 20:11, 5 June 2023
also Fourier's proof that e is irrational.) Furthermore, by the Lindemann–Weierstrass theorem, e is transcendental, meaning that it is not a solution...
53 KB (6,452 words) - 22:09, 21 August 2024
Lindemann–Weierstrass theorem (redirect from Proof that e is transcendental)
contradiction which completes the proof. ∎ Note that Lemma A is sufficient to prove that e is irrational, since otherwise we may write e = p / q, where both p and...
28 KB (4,823 words) - 00:37, 7 November 2023
ring is a field Four proofs of the Basel problem Proof that e is irrational (also showing the irrationality of certain related numbers) Hilbert's third problem...
5 KB (454 words) - 06:52, 11 July 2024
In mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for...
14 KB (2,073 words) - 11:54, 4 April 2024
List of exponential topics (category Short description is different from Wikidata)
key frequencies p-adic exponential function Power law Proof that e is irrational Proof that e is transcendental Q-exponential Radioactive decay Rule of...
6 KB (281 words) - 08:56, 22 January 2024
Characterizations of the exponential function (redirect from Proof of e as a limit)
factorial of n. One proof that e is irrational uses a special case of this formula.) Inverse of logarithm integral. Define e x {\displaystyle e^{x}} to be the...
22 KB (4,715 words) - 07:41, 23 June 2024
Predictably Irrational: The Hidden Forces That Shape Our Decisions is a 2008 book by Dan Ariely, in which he challenges readers' assumptions about making...
19 KB (2,709 words) - 12:03, 16 October 2023
Elements also covers number theory, including a proof that the square root of two is irrational and a proof that there are infinitely many prime numbers. Further...
38 KB (4,783 words) - 16:48, 14 August 2024
Square root of 2 (redirect from Proof that the square root of 2 is irrational)
natural number that is not a perfect square is irrational. For other proofs that the square root of any non-square natural number is irrational, see Quadratic...
39 KB (5,570 words) - 13:21, 20 August 2024
Proofs of the mathematical result that the rational number 22/7 is greater than π (pi) date back to antiquity. One of these proofs, more recently developed...
13 KB (2,784 words) - 13:00, 26 July 2024
Euler's identity (redirect from E^πi)
addition, it is directly used in a proof that π is transcendental, which implies the impossibility of squaring the circle. Euler's identity is often cited...
16 KB (1,963 words) - 00:15, 21 August 2024
List of number theory topics (category Short description is different from Wikidata)
Transcendental number e (mathematical constant) pi, list of topics related to pi Squaring the circle Proof that e is irrational Lindemann–Weierstrass...
10 KB (935 words) - 23:13, 8 August 2024
Euler's formula (redirect from E^ix)
means. Various proofs of the formula are possible. This proof shows that the quotient of the trigonometric and exponential expressions is the constant function...
26 KB (3,832 words) - 03:31, 6 August 2024
mathematics, a quadratic irrational number (also known as a quadratic irrational or quadratic surd) is an irrational number that is the solution to some quadratic...
11 KB (1,627 words) - 22:45, 17 March 2024
what later became a very extensive theory. The proof that the square root of 2 (√2) is irrational (i.e. cannot be expressed as a fraction of two whole...
15 KB (2,223 words) - 11:42, 29 July 2024
Half-life (category Pages that use a deprecated format of the chem tags)
{1}{t_{2}}}+{\frac {1}{t_{3}}}+\cdots } For a proof of these formulas, see Exponential decay § Decay by two or more processes. There is a half-life describing any exponential-decay...
17 KB (2,182 words) - 21:20, 12 August 2024
Compound interest (category Pages that use a deprecated format of the math tags)
interest is interest accumulated from a principal sum and previously accumulated interest. It is the result of reinvesting or retaining interest that would...
18 KB (2,592 words) - 04:27, 15 August 2024
In logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition...
19 KB (2,501 words) - 08:22, 2 August 2024
Leonhard Euler (category Short description is different from Wikidata)
Frenchman. Diderot was informed that a learned mathematician had produced a proof of the existence of God: he agreed to view the proof as it was presented in court...
102 KB (10,269 words) - 21:16, 9 July 2024
Schanuel's conjecture (category Short description is different from Wikidata)
a generalised period conjecture includes Schanuel's conjecture. While a proof of Schanuel's conjecture seems a long way off, connections with model theory...
10 KB (1,173 words) - 08:45, 7 November 2023
Natural logarithm (redirect from Base-e logarithm)
The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately...
37 KB (6,116 words) - 23:38, 24 August 2024
Liouville number (redirect from Measure of irrationality)
Proof of assertion: As a consequence of this lemma, let x be a Liouville number; as noted in the article text, x is then irrational. If x is algebraic...
33 KB (5,109 words) - 14:21, 23 August 2024
propositions in logic. The irrationality of the square root of 2 is one of the oldest proofs of impossibility. It shows that it is impossible to express the...
29 KB (3,909 words) - 08:17, 2 August 2024
Transcendental number (category Articles containing proofs)
that e and π were both transcendental numbers in his 1768 paper proving the number π is irrational, and proposed a tentative sketch proof that π is transcendental...
51 KB (6,761 words) - 13:32, 23 August 2024
{2}}}={\sqrt {2}}^{2}=2} is an irrational to an irrational power that is a rational which proves the theorem. The proof is not constructive, as it does...
5 KB (559 words) - 03:42, 8 June 2024