Sufficiently large - Citizendia

In mathematics, the phrase sufficiently large is used in contexts such as:

P

is true for sufficiently large

x

which is actually shorthand for:

there exists an $a\in\mathbb{R}$ such that

P

is true for all $x\ge a$ . Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and

This does not necessarily mean that any particular value for $a$ is known, but only that such an $a$ exists. The phrase "sufficiently large" should not be confused with the phrases "arbitrarily large" or "infinitely large". In Mathematics, the phrase arbitrarily large, arbitrarily small, arbitrarily long is used in statements such as "&fnof( x Infinity (symbolically represented with ∞) comes from the Latin infinitas or "unboundedness

"Sufficiently large" is sometimes the subject of mathematical humor; for example, as in the mathematician's joke "π = 3, for sufficiently large values of 3". A mathematical joke is a form of Humor which relies on aspects of Mathematics or a Stereotype of Mathematicians to Derive humor

Other uses in mathematics

A Haken manifold is sometimes called sufficiently large. In Mathematics, a Haken manifold is a compact, P²-irreducible 3-manifold that contains a two-sided Incompressible surface

Other uses in mathematics

See also