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Lecture 1
... Proof: Suppose (for a contradiction) that there are only finitely many prime numbers p1 < p2 < . . . < pn . Consider the positive integer q = p1 p2 · · · pn + 1. q is greater than pn so cannot be prime, and so is divisible by some prime p1 , p2 , . . . , pn . But dividing q by any of these primes le ...
... Proof: Suppose (for a contradiction) that there are only finitely many prime numbers p1 < p2 < . . . < pn . Consider the positive integer q = p1 p2 · · · pn + 1. q is greater than pn so cannot be prime, and so is divisible by some prime p1 , p2 , . . . , pn . But dividing q by any of these primes le ...
File
... The Density Property of real numbers states that between any two real numbers is another real number. This property is also true for rational numbers, but not for whole numbers or integers. For instance, there is no integer between –2 and –3. ...
... The Density Property of real numbers states that between any two real numbers is another real number. This property is also true for rational numbers, but not for whole numbers or integers. For instance, there is no integer between –2 and –3. ...
appendix B
... floating point number that can be represented in this system. o Previously, most hardware took 1 of 2 approaches: just set the result to 0 and continue, or cause a floating point underflow trap. Neither of these is really satisfactory, so IEEE invented denormalized numbers. These numbers have an e ...
... floating point number that can be represented in this system. o Previously, most hardware took 1 of 2 approaches: just set the result to 0 and continue, or cause a floating point underflow trap. Neither of these is really satisfactory, so IEEE invented denormalized numbers. These numbers have an e ...
1. Number Sense, Properties, and Operations
... c. Perform arithmetic operations with complex numbers. (CCSS: N-CN) i. Define the complex number i such that i2 = –1, and show that every complex number has the form a + bi where a and b are real numbers. (CCSS: N-CN.1) ii. Use the relation i2 = –1 and the commutative, associative, and distributive ...
... c. Perform arithmetic operations with complex numbers. (CCSS: N-CN) i. Define the complex number i such that i2 = –1, and show that every complex number has the form a + bi where a and b are real numbers. (CCSS: N-CN.1) ii. Use the relation i2 = –1 and the commutative, associative, and distributive ...
Square Roots - Mr. Hooks Math
... have finite (ends) number of digits. (ex 2/5= 0.40 ) • Repeating decimal -rational numbers in decimal form that have a block for one or more digits that repeats continuously. (ex. 1.3=1.333333333) • Irrational numbers - numbers that cannot be expressed as a fraction including square roots of whole n ...
... have finite (ends) number of digits. (ex 2/5= 0.40 ) • Repeating decimal -rational numbers in decimal form that have a block for one or more digits that repeats continuously. (ex. 1.3=1.333333333) • Irrational numbers - numbers that cannot be expressed as a fraction including square roots of whole n ...
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.