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When is a number Fibonacci? - Department of Computer Science
When is a number Fibonacci? - Department of Computer Science

1.1.1 Introduction to Axiomatic Systems
1.1.1 Introduction to Axiomatic Systems

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... Convert the distribution to a ‘less than’ type cumulative frequency distribution. Then taking a suitable scale draw its ogive on a graph paper provided. ...
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Studying prime numbers with Maple

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ASSESSMENT TASK NOTIFICATION Student Name

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... Check that n sqrt(2) is a positive integer: It’s clearly positive, and it can be written as (m – n) sqrt(2) = m sqrt(2) – n sqrt (2) = (n sqrt(2)) sqrt(2) – m = 2n – m. So the idea of the proof is that if sqrt(2) were equal to some fraction, like 17/12, then it would have to be equal to the simple ...
[Write on board:
[Write on board:

... Check that n sqrt(2) is a positive integer: It’s clearly positive, and it can be written as (m – n) sqrt(2) = m sqrt(2) – n sqrt (2) = (n sqrt(2)) sqrt(2) – m = 2n – m. So the idea of the proof is that if sqrt(2) were equal to some fraction, like 17/12, then it would have to be equal to the simple ...
number fields
number fields

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... 1) (x3 – 2x2 + 2x – 6) ÷ (x - 3) x2 + x + 5 + 9/(x-3) 2) (3x4 + x3 – 8x2 + 10x – 3) ÷ (3x - 2) x3 + x2 - 2x + 2 + 1/(3x-2) ...
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Linear Transformations Ch.12

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Algebraic Elimination of epsilon-transitions

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Simplifying Expressions Involving Radicals

... the depth over Q of the left-hand side of Ramanujan’s equations is 2 while the depth of the right-hand side is 1. If we are given a nested radical and are asked to denest it then this is at first not a meaningful question because for different values roots inq√ of the q ...
Algebra I Notes
Algebra I Notes

... Like the counting numbers, the integers are closed under addition and multiplication. Similarly, when you subtract one integer from another, the answer is always an integer. That is, the integers are also closed under subtraction. Rational numbers The set of rational numbers includes all integers an ...
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Free groups

< 1 ... 96 97 98 99 100 101 102 103 104 ... 480 >

Fundamental theorem of algebra

The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with an imaginary part equal to zero.Equivalently (by definition), the theorem states that the field of complex numbers is algebraically closed.The theorem is also stated as follows: every non-zero, single-variable, degree n polynomial with complex coefficients has, counted with multiplicity, exactly n roots. The equivalence of the two statements can be proven through the use of successive polynomial division.In spite of its name, there is no purely algebraic proof of the theorem, since any proof must use the completeness of the reals (or some other equivalent formulation of completeness), which is not an algebraic concept. Additionally, it is not fundamental for modern algebra; its name was given at a time when the study of algebra was mainly concerned with the solutions of polynomial equations with real or complex coefficients.
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