Sufficiently large
Encyclopedia
In mathematics
, the phrase sufficiently large is used in contexts such as:
is true for sufficiently large 
which is actually shorthand for:
such that 
is true 
.
This does not necessarily mean that any particular value for
is known, but only that such an 
exists. The phrase "sufficiently large" should not be confused with the phrases "arbitrarily large
" or "infinitely
large".
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the phrase sufficiently large is used in contexts such as:
is true for sufficiently large which is actually shorthand for:
such that is true .This does not necessarily mean that any particular value for
is known, but only that such an exists. The phrase "sufficiently large" should not be confused with the phrases "arbitrarily largeArbitrarily large
In mathematics, the phrase arbitrarily large, arbitrarily small, arbitrarily long is used in statements such as:which is shorthand for:This should not be confused with the phrase "sufficiently large"...
" or "infinitely
Infinity
Infinity is a concept in many fields, most predominantly mathematics and physics, that refers to a quantity without bound or end. People have developed various ideas throughout history about the nature of infinity...
large".
Other uses in mathematics
- A sufficiently large manifold is a manifold containing a properly embedded 2-sided incompressible surface.