(G′/G)-expansion method
The (G′/G)-expansion method is an ansatz technique that finds exact traveling wave solutions of nonlinear evolution equations by expanding the solution as a polynomial in G′/G, where G satisfies a second-order linear ordinary differential equation.
(ε, δ)-definition of limit
The (ε, δ)-definition of limit is the formal definition of the limit of a function in calculus, stating that f(x) can be made arbitrarily close to L.
−2
−2, known as negative two or minus 2, is the additive inverse of 2, an even integer lying two units to the left of zero on the number line.
0.999...
0.999..., the repeating decimal with an unending string of nines, is exactly equal to the integer 1 in the real number system, a standard fact that many students find counterintuitive.
1
1, one, or unity, is the first positive integer and an odd number that leaves every number unchanged when multiplying, and is neither prime nor composite in modern mathematics.
1 + 2 + 3 + 4 + ⋯
The series 1 + 2 + 3 + 4 + ⋯, the sum of all natural numbers, diverges, but is assigned the value −1/12 in analytic continuation.
1,000,000
1,000,000 (one million, ten lakh) is the natural number equal to 10 to the 6th power, the first named number above a thousand in the English short scale.
1,000,000,000
1,000,000,000, called one billion or one thousand million, is the number 10 to the ninth power, matching the SI prefix giga, as in gigawatt and gigahertz.
1,000,000,000,000
1,000,000,000,000 is the number 10 to the 12th power, a one followed by twelve zeros, called one trillion on the short scale and one billion on the long scale.
1/2 + 1/4 + 1/8 + 1/16 + ⋯
The series 1/2 + 1/4 + 1/8 + 1/16 + ⋯ is an infinite geometric series whose sum is exactly 1, since each term is half the one before it.
10
10 (ten) is the even natural number following 9 and preceding 11, serving as the base of the decimal numeral system used for counting and measurement.
10,000,000,000
10,000,000,000 (ten billion, or 10 to the 10th) is the natural number written as a 1 followed by ten zeros, equal to ten thousand million.
100
100, also called a short hundred, is the square of 10, a Harshad and abundant number with nine divisors, and the atomic number of the element fermium.
100,000
100,000, also written one hundred thousand, is the natural number equal to 10 to the fifth power; in the Indian numbering system it is called one lakh.
1000 (number)
1000, one thousand, is the natural number equal to 10³, the base of the SI prefix kilo and the value of the Roman numeral M.
101 (number)
101 is the natural number after 100, a palindromic prime and the 26th prime number, widely known in the United States as the label for introductory college courses.
108 (number)
108 is the natural number following 107 and preceding 109, with prime factorization 2² × 3³, and a sacred number in Hindu and Buddhist practice.
11 (number)
11 (eleven) is the natural number following 10 and preceding 12. It is the fifth prime, a palindromic prime, the smallest two-digit prime, and the atomic number of sodium.
11:11 (numerology)
11:11 is a clock time treated in numerology as an angel number signaling alignment or awakening, and in popular custom as a moment to make a wish, occurring twice daily.
12 (number)
12 is the natural number after 11 and before 13, a highly composite number with six divisors that underlies the dozen, the hour, and the 12-month calendar.
120-cell
The 120-cell, also called the hecatonicosachoron or hyperdodecahedron, is a convex regular four-dimensional polytope of 120 dodecahedral cells, discovered by Ludwig Schläfli and dual to the 600-cell.
13 (number)
13 (thirteen) is the natural number after 12, the sixth prime number, a Fibonacci number, the atomic number of aluminum, and a traditional symbol of bad luck in the West.
14 (number)
The number 14 is a composite number used in chemistry as silicon's atomic number and in mathematics as the fourth Catalan number and the smallest even nontotient.
15 (number)
15 (fifteen) is the natural number following 14, the product of the primes 3 and 5, and the fifth triangular number, with atomic number 15 being phosphorus.
16 (number)
16, sixteen, is the natural number after 15 and the fourth power of 2, serving as the base of hexadecimal, the compact shorthand computers use for binary data.
16-cell
The 16-cell, also called the hexadecachoron, is the regular four-dimensional cross polytope, the 4D analog of the octahedron, bounded by 16 tetrahedral cells and dual to the tesseract.
17 (number)
17, or seventeen, is the seventh prime number and third Fermat prime; Gauss proved in 1796 that the regular 17-gon is constructible, and chlorine has atomic number 17.
1729 (number)
The number 1729, the Hardy–Ramanujan number, is the smallest integer expressible as a sum of two positive cubes in two ways: 1³ + 12³ = 9³ + 10³.
18 (number)
18 (eighteen; Roman numeral XVIII) is the natural number following 17 and preceding 19, known as the age of legal adulthood and the holes in a golf round.
19 (number)
19, or nineteen, is the eighth prime number, known for the 19-year Metonic cycle of the Moon, Waring's constant, and the prime field of Curve25519.