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What are some examples of Injection Surjection and Bijection?
Too long to explain so just go here http://en.wikipedia.org/wiki/Bijection,_injection_and_surjection
Is a monotonic function a bijection?
No. For example, y = 7 is monotonic. It may be a degenerate case, but that does not disallow it. It is not a bijection unless the domain and range are sets with cardinality 1. Even a function that is strictly monotonic need not be a bijection. For example, y = sqrt(x) is strictly monotonic [increasing] for all non-negative x. But it is not a bijection from the set of real numbers to the set of real numbers because it is not defined for negative x.
When does a relation be a function?
A function is a relation whose mapping is a bijection.
What is the difference between relations and functions?
A function is a relation whose mapping is a bijection.
Is every bijection a strictly monotonic function?
No. For example, consider the discontinuous bijection that increases linearly from [0,0] to [1,1], decreases linearly from (1,2) to (2,1), increases linearly from [2,2] to [3,3], decreases linearly from (3,4) to (4,3), etc.
What is bijection?
A bijection is a one-to-one correspondence in set theory - a function which is both a surjection and an injection.
Does the greatest integer function have an inverse function?
Inverse of a function exists only if it is a Bijection. Bijection=Injection(one to one)+surjection (onto) function.
What are some examples of Injection Surjection and Bijection?
Too long to explain so just go here http://en.wikipedia.org/wiki/Bijection,_injection_and_surjection
Is a monotonic function a bijection?
No. For example, y = 7 is monotonic. It may be a degenerate case, but that does not disallow it. It is not a bijection unless the domain and range are sets with cardinality 1. Even a function that is strictly monotonic need not be a bijection. For example, y = sqrt(x) is strictly monotonic [increasing] for all non-negative x. But it is not a bijection from the set of real numbers to the set of real numbers because it is not defined for negative x.
When does a relation be a function?
A function is a relation whose mapping is a bijection.
What is the correspondence of the domain and range of a linear function?
It is a bijection [one-to-one and onto].
What is the difference between relations and functions?
A function is a relation whose mapping is a bijection.
Is every bijection a strictly monotonic function?
No. For example, consider the discontinuous bijection that increases linearly from [0,0] to [1,1], decreases linearly from (1,2) to (2,1), increases linearly from [2,2] to [3,3], decreases linearly from (3,4) to (4,3), etc.
What is a bijective numeration?
A bijective numeration is a numeral system which uses digits to establish a bijection between finite strings and the positive integers.
What words have two J's in it?
Some words that have two J's include "jujitsu", "hijinks", and "bijection".
Is every permutation always a one-to-one function?
By definition, a permutation is a bijection from a set to itself. Since a permutation is bijective, it is one-to-one.
Why does multiplication by 2 define a bijection from R to R R meaning set of Real numbers but not from Z to Z Z meaning set of integers?
It's not a bijection in Z because it's not surjective. For example, f(x) = 3 has no solution in Z. In other words, you can't double an integer (Z) to get an odd number. It works in R because it's ok to have decimals.
