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The Three Point Pick Problem on the Bidisk
The Three Point Pick Problem on the Bidisk

... geodesic disk passing through 1 and 2 , but will not be unique o this disk. (For the example 1 = (0 0) 2 = ( 12  12 ) w1 = 0 w2 = 21 , on the diagonal f(z z )g we must have (z z ) = z  but o the diagonal any convex combination of the two coordinate functions z 1 and z 2 will work). It ...
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CS103X: Discrete Structures Homework Assignment 2: Solutions

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SectionGroups

... 1. Determine whether the binary operation  defined on the following sets represent a group. If not a group, state a reason why. a. Let  be defined on Z by letting a  b  ab . b. Let  be defined on 2 Z by letting a  b  a  b . c. Let  be defined on R  by letting a  b  ab . d. Let  be defin ...
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Topics in Logic and Proofs

... We have seen that a logic operator, such as p → q, is defined by its truth table. In other words, a different table gives a different logic operator. Question. How many different logic operators involving p and q are possible? There is no doubt, however, that some of these operators are actually int ...
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Solutions 8 - D-MATH

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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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