Lecture 10: Prime numbers
... prime numbers. For example, 6 = 3 + 3, 12 = 5 + 7, 100 = 47 + 53. This was proposed in 1742 by Christian Goldbach, and has now been verified for numbers up to 4 × 1018 . A recent paper (May 2013) by Harald Helfgott has shown that every odd number greater than 5 is the sum of at most three primes: ht ...
... prime numbers. For example, 6 = 3 + 3, 12 = 5 + 7, 100 = 47 + 53. This was proposed in 1742 by Christian Goldbach, and has now been verified for numbers up to 4 × 1018 . A recent paper (May 2013) by Harald Helfgott has shown that every odd number greater than 5 is the sum of at most three primes: ht ...
computer applications - IndiaStudyChannel.com
... 7. Accept the names of 'n' animals in a one dimentional array. Sort these animals alphabetically using the Bubble Sort technique only. [Eg: If inputs= Cow, Cockroach, Crow, Cat, Camel, Calf, Centipede. outputs= Calf, Camel, Cat, Centipede, Cockroach, Cow, Crow.] [15] 8. Use a constructor to accept a ...
... 7. Accept the names of 'n' animals in a one dimentional array. Sort these animals alphabetically using the Bubble Sort technique only. [Eg: If inputs= Cow, Cockroach, Crow, Cat, Camel, Calf, Centipede. outputs= Calf, Camel, Cat, Centipede, Cockroach, Cow, Crow.] [15] 8. Use a constructor to accept a ...
Discrete Math
... 4. Three dice are thrown. Each dice can have a square with one of {1, 2, 3, 4, 5, 6} facing up. (a) How many different possibilities are there for the numbers facing up with different colored dice? (b) How many possibilities are there with two kinds of dice? (c) How many different multisets of 3 num ...
... 4. Three dice are thrown. Each dice can have a square with one of {1, 2, 3, 4, 5, 6} facing up. (a) How many different possibilities are there for the numbers facing up with different colored dice? (b) How many possibilities are there with two kinds of dice? (c) How many different multisets of 3 num ...
Solutions to Problem Set #2
... Elaborate variants of the idea have been used to study the distribution of primes ever since Euler. Ultimately this line of thought leads to the Riemann zeta-function, and to the most famous unsolved problem in mathematics, the Riemann Hypothesis. Comment. We operated with infinite sums as if they w ...
... Elaborate variants of the idea have been used to study the distribution of primes ever since Euler. Ultimately this line of thought leads to the Riemann zeta-function, and to the most famous unsolved problem in mathematics, the Riemann Hypothesis. Comment. We operated with infinite sums as if they w ...
Positive and Negative Numbers
... We know when we see positive numbers, but when do we use or see negative numbers? ...
... We know when we see positive numbers, but when do we use or see negative numbers? ...
HERE
... real numbers give us all possible slopes, except for the vertical line. When x 0 , all the points in the equivalence class lie on the vertical line that is the y-axis. (Again the origin must be excluded from this equivalence class.) The ratio of the coordinates is undefined, so the slope is undefi ...
... real numbers give us all possible slopes, except for the vertical line. When x 0 , all the points in the equivalence class lie on the vertical line that is the y-axis. (Again the origin must be excluded from this equivalence class.) The ratio of the coordinates is undefined, so the slope is undefi ...
Infinity
Infinity (symbol: ∞) is an abstract concept describing something without any limit and is relevant in a number of fields, predominantly mathematics and physics.In mathematics, ""infinity"" is often treated as if it were a number (i.e., it counts or measures things: ""an infinite number of terms"") but it is not the same sort of number as natural or real numbers. In number systems incorporating infinitesimals, the reciprocal of an infinitesimal is an infinite number, i.e., a number greater than any real number; see 1/∞.Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. In the theory he developed, there are infinite sets of different sizes (called cardinalities). For example, the set of integers is countably infinite, while the infinite set of real numbers is uncountable.