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Irrational numbers
... Irrational numbers can be written only as decimals that do not terminate or repeat. They cannot be written as the quotient of two integers. If a whole number is not a perfect square, then its square root is an irrational number. For example, 2 is not a perfect square, so 2 is irrational. Caution! A ...
... Irrational numbers can be written only as decimals that do not terminate or repeat. They cannot be written as the quotient of two integers. If a whole number is not a perfect square, then its square root is an irrational number. For example, 2 is not a perfect square, so 2 is irrational. Caution! A ...
Direct Proof
... The simplest and most straightforward type of proof is a “direct” proof, which we’ll call any proof that follows straight from the definitions or from a direct calculation. Here’s a couple of examples: First we’ll prove the following statement: The sum of any two rational numbers is rational. This p ...
... The simplest and most straightforward type of proof is a “direct” proof, which we’ll call any proof that follows straight from the definitions or from a direct calculation. Here’s a couple of examples: First we’ll prove the following statement: The sum of any two rational numbers is rational. This p ...
Hindawi Publishing Corporation EURASIP Journal on Bioinformatics and Systems Biology
... Arithmetic in Fqn , q prime, is integer arithmetic modulo q. Arithmetic in Fqn is efficiently performed by table lookup methods, as shown below. Nonzero elements of Fqn are represented by powers of a primitive element α. Multiplication is then performed by adding exponents modulo qn − 1. For addition ...
... Arithmetic in Fqn , q prime, is integer arithmetic modulo q. Arithmetic in Fqn is efficiently performed by table lookup methods, as shown below. Nonzero elements of Fqn are represented by powers of a primitive element α. Multiplication is then performed by adding exponents modulo qn − 1. For addition ...
LINEAR EQUATIONS WITH UNKNOWNS FROM A
... J be the corresponding subset of {1, . . . , h}, and u0 ∈ Qr the corresponding vector, such that (2.3) holds. We distinguish two cases. First suppose that J is contained in some set Il . Then the elements aj (j ∈ J) are linearly dependent over k. There is a proper subset J 0 of J such that aj (j ∈ J ...
... J be the corresponding subset of {1, . . . , h}, and u0 ∈ Qr the corresponding vector, such that (2.3) holds. We distinguish two cases. First suppose that J is contained in some set Il . Then the elements aj (j ∈ J) are linearly dependent over k. There is a proper subset J 0 of J such that aj (j ∈ J ...
Solutions Sheet 7
... 5. Let X be a locally noetherian scheme. Prove that the set of irreducible components of X is locally finite, i.e. that every point of X has an open neighborhood which meets only finitely many irreducible components of X. Solution: By definition the irreducible components of a topological space are ...
... 5. Let X be a locally noetherian scheme. Prove that the set of irreducible components of X is locally finite, i.e. that every point of X has an open neighborhood which meets only finitely many irreducible components of X. Solution: By definition the irreducible components of a topological space are ...
