How do you use Bijection in a sentence? See 10+ example sentences showing how this word appears in different contexts, plus the exact meaning.
Bijection meaning
A one-to-one correspondence, a function which is both a surjection and an injection.
Using Bijection
- The main meaning on this page is: A one-to-one correspondence, a function which is both a surjection and an injection.
- In the example corpus, bijection often appears in combinations such as: is bijection, bijection between, bijection is.
Context around Bijection
- Average sentence length in these examples: 23.2 words
- Position in the sentence: 3 start, 8 middle, 9 end
- Sentence types: 20 statements, 0 questions, 0 exclamations
Corpus analysis for Bijection
- In this selection, "bijection" usually appears near the end of the sentence. The average example has 23.2 words, and this corpus slice is mostly made up of statements.
- Around the word, required, linear and defined stand out and add context to how "bijection" is used.
- Recognizable usage signals include is a bijection and the required bijection. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "bijection" sits close to words such as abadi, acidification and acker, which helps place it inside the broader word index.
Example types with bijection
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
In both cases, therefore, Df x fails to be a bijection. (11 words)
A function is invertible if and only if it is a bijection. (12 words)
Recall that to prove this we need to exhibit a bijection between them. (13 words)
But, to each algorithm, there may or may not correspond a real number, as the algorithm may fail to satisfy the constraints, or even be non-terminating (T is a partial function ), so this fails to produce the required bijection. (40 words)
And in fact, Cantor's diagonal argument is constructive, in the sense that given a bijection between the real numbers and natural numbers, one constructs a real number that doesn't fit, and thereby proves a contradiction. (37 words)
Polyadic or multiary means n-ary for some nonnegative integer n. A 0-ary, or nullary, quasigroup is just a constant element of Q. A 1-ary, or unary, quasigroup is a bijection of Q to itself. (37 words)
Example sentences (20)
To build a bijection from T to R: start with the tangent function tan(x), which provides a bijection from (−π/2, π/2) to R; see right picture.
With this terminology, a bijection is a function which is both a surjection and an injection, or using other words, a bijection is a function which is both "one-to-one" and "onto".
A function is invertible if and only if it is a bijection.
A homeomorphism is a bijection that is continuous and whose inverse is also continuous.
And in fact, Cantor's diagonal argument is constructive, in the sense that given a bijection between the real numbers and natural numbers, one constructs a real number that doesn't fit, and thereby proves a contradiction.
Any surjective function induces a bijection defined on a quotient of its domain by collapsing all arguments mapping to a given fixed image.
As a vector space The bijection between points on the real line and vectors.
But, to each algorithm, there may or may not correspond a real number, as the algorithm may fail to satisfy the constraints, or even be non-terminating (T is a partial function ), so this fails to produce the required bijection.
Cardinality of infinite sets main Two sets are said to have the same cardinality or cardinal number if there exists a bijection (a one-to-one correspondence) between them.
Composition The composition of two bijections f: X → Y and g: Y → Z is a bijection.
Definition Given two manifolds M and N, a differentiable map f : M → N is called a diffeomorphism if it is a bijection and its inverse f −1 : N → M is differentiable as well.
However this reasoning is not constructive, as it still does not construct the required bijection.
If X and Y are normed spaces, they are isomorphic normed spaces if there exists a linear bijection T : X → Y such that T and its inverse T −1 are continuous.
In both cases, therefore, Df x fails to be a bijection.
In other words, a total order on a set with k elements induces a bijection with the first k natural numbers.
In particular, the Cantor set is in bijection with the set of binary sequences.
More precisely, every surjection f : A → B can be factored as a projection followed by a bijection as follows.
One way to prove that a class is proper is to place it in bijection with the class of all ordinal numbers.
Polyadic or multiary means n-ary for some nonnegative integer n. A 0-ary, or nullary, quasigroup is just a constant element of Q. A 1-ary, or unary, quasigroup is a bijection of Q to itself.
Recall that to prove this we need to exhibit a bijection between them.
Common combinations with bijection
These word pairs occur most frequently in English texts:
- is bijection 7×
- bijection between 7×
- bijection is 3×
- bijection with 3×
- bijection from 2×
- induces bijection 2×
- required bijection 2×
- in bijection 2×
- bijection of 2×