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  2. Large numbers - Wikipedia

    en.wikipedia.org/wiki/Large_numbers

    A function with a vertical asymptote is not helpful in defining a very large number, although the function increases very rapidly: one has to define an argument very close to the asymptote, i.e. use a very small number, and constructing that is equivalent to constructing a very large number, e.g. the reciprocal.

  3. Graham's number - Wikipedia

    en.wikipedia.org/wiki/Graham's_number

    Graham's number is an immense number that arose as an upper bound on the answer of a problem in the mathematical field of Ramsey theory.It is much larger than many other large numbers such as Skewes's number and Moser's number, both of which are in turn much larger than a googolplex.

  4. Rouché's theorem - Wikipedia

    en.wikipedia.org/wiki/Rouché's_theorem

    Since has zeros inside the disk | | < (because >), it follows from Rouché's theorem that also has the same number of zeros inside the disk. One advantage of this proof over the others is that it shows not only that a polynomial must have a zero but the number of its zeros is equal to its degree (counting, as usual, multiplicity).

  5. Knuth's up-arrow notation - Wikipedia

    en.wikipedia.org/wiki/Knuth's_up-arrow_notation

    In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. [1]In his 1947 paper, [2] R. L. Goodstein introduced the specific sequence of operations that are now called hyperoperations.

  6. Rational root theorem - Wikipedia

    en.wikipedia.org/wiki/Rational_root_theorem

    It gives a finite number of possible fractions which can be checked to see if they are roots. If a rational root x = r is found, a linear polynomial ( x – r ) can be factored out of the polynomial using polynomial long division , resulting in a polynomial of lower degree whose roots are also roots of the original polynomial.

  7. Bézout's theorem - Wikipedia

    en.wikipedia.org/wiki/Bézout's_theorem

    Bézout's theorem is a statement in algebraic geometry concerning the number of common zeros of n polynomials in n indeterminates. In its original form the theorem states that in general the number of common zeros equals the product of the degrees of the polynomials. [1] It is named after Étienne Bézout.

  8. Zeros and poles - Wikipedia

    en.wikipedia.org/wiki/Zeros_and_poles

    Because of the order of zeros and poles being defined as a non-negative number n and the symmetry between them, it is often useful to consider a pole of order n as a zero of order –n and a zero of order n as a pole of order –n. In this case a point that is neither a pole nor a zero is viewed as a pole (or zero) of order 0.

  9. Zero of a function - Wikipedia

    en.wikipedia.org/wiki/Zero_of_a_function

    The fundamental theorem of algebra shows that any non-zero polynomial has a number of roots at most equal to its degree, and that the number of roots and the degree are equal when one considers the complex roots (or more generally, the roots in an algebraically closed extension) counted with their multiplicities. [3]