Notes
... the reals, R, and ordinary calculus over the “classical” reals 1. In calculus books, the operations on the reals are not defined by algorithms. Indeed we imagine that we can say things in calculus that don’t make sense computationally. For example, in calculus we assume that given two reals, say r1 ...
... the reals, R, and ordinary calculus over the “classical” reals 1. In calculus books, the operations on the reals are not defined by algorithms. Indeed we imagine that we can say things in calculus that don’t make sense computationally. For example, in calculus we assume that given two reals, say r1 ...
Complex Numbers ). sin (cos
... Calculator MODES for calculation results. (Complex numbers can be entered in any form, no matter the mode. Output is controlled by the MODE selected.) Your calculator can perform all operations of complex numbers (adding, multiplying, raising to powers and taking roots - although only one root is r ...
... Calculator MODES for calculation results. (Complex numbers can be entered in any form, no matter the mode. Output is controlled by the MODE selected.) Your calculator can perform all operations of complex numbers (adding, multiplying, raising to powers and taking roots - although only one root is r ...
PDF
... Then F is the field of constructible numbers. Note that E ⊂ F. Moreover, F ∩ R = E. An element of F is called a constructible number. These numbers can be “constructed” by a process that will be described shortly. Conversely, let us start with a subset S of C such that S contains a non-zero complex ...
... Then F is the field of constructible numbers. Note that E ⊂ F. Moreover, F ∩ R = E. An element of F is called a constructible number. These numbers can be “constructed” by a process that will be described shortly. Conversely, let us start with a subset S of C such that S contains a non-zero complex ...
Graphing Complex Numbers
... numbers: one for the real part and one for the imaginary part. We call these the real axis and the imaginary axis, respectively. The plane determined by these two axes is called the complex plane. ...
... numbers: one for the real part and one for the imaginary part. We call these the real axis and the imaginary axis, respectively. The plane determined by these two axes is called the complex plane. ...
Full text
... Perhaps an even more difficult problem exists in the question whether numbers not of the form 9n±4 can be expressed as the sum of three cubes; that is, does the equation A3 + B3 + C3 = k ...
... Perhaps an even more difficult problem exists in the question whether numbers not of the form 9n±4 can be expressed as the sum of three cubes; that is, does the equation A3 + B3 + C3 = k ...
Set-Builder Notation
... expressed as the quotient of two integers, a, b, b ≠ 0. {a/b | a and b are integers, b ≠ 0} – Irrational numbers: any number that CANNOT be expressed as the quotient of two integers. – Real numbers: any number that lies on the number line. ...
... expressed as the quotient of two integers, a, b, b ≠ 0. {a/b | a and b are integers, b ≠ 0} – Irrational numbers: any number that CANNOT be expressed as the quotient of two integers. – Real numbers: any number that lies on the number line. ...
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.