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...

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...

In mathematics, the irrational numbers (in- + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed...

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...

also Fourier's proof that e is irrational.) Furthermore, by the Lindemann–Weierstrass theorem, e is transcendental, meaning that it is not a solution...

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...

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...

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...

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...

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...