Modern Problems of Mathematical Analysis

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Across
  1. 3. In mathematics, an _________ function is a function that maps distinct elements of its domain to distinct elements of its codomain.
  2. 5. it is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns
  3. 7. it is a collection of well defined and distinct objects
  4. 8. it is a polynomial that is the sum of two terms, each of which is a monomial.
  5. 9. it is an enumerated collection of objects in which repetitions are allowed and order matters
  6. 12. it is a finite combination of symbols that is well-formed according to rules that depend on the context
  7. 15. it is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
  8. 17. In mathematics, a _______ function is a function between ordered sets that preserves or reverses the given order.
Down
  1. 1. A _______ is a statement that can be demonstrated to be true by accepted mathematical operations and arguments.
  2. 2. it is a set together with a metric on the set
  3. 4. In mathematics, specifically set theory, the ______ _________ of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a is in A and b is in B.
  4. 6. In mathematics, a ______ is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.
  5. 9. it is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements
  6. 10. it is a binary relation between two sets that associates every element of the first set to exactly one element of the second set
  7. 11. it is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression
  8. 13. In mathematics, a function f from a set X to a set Y is _______ , if for every element y in the codomain Y of f, there is at least one element x in the domain X of f such that f(x) = y.
  9. 14. it is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables
  10. 16. it is the value that a function "approaches" as the input "approaches" some value