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playa007
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Homework Statement
Is it possible to find a non-bijective function from the integers to the integers such that:
f(j+n)=f(j)+n where n is a fixed integer greater than or equal to 1 and j arbitrary integer.
A non-bijective function from integers to integers is a mathematical function that maps a set of integers to another set of integers, but is not a one-to-one correspondence. This means that there are some elements in the output set that do not have a corresponding element in the input set.
A bijective function is a one-to-one correspondence between two sets, meaning that each element in the input set has a unique corresponding element in the output set, and vice versa. In contrast, a non-bijective function does not have this one-to-one correspondence, and some elements in the output set may have multiple corresponding elements in the input set.
Yes, a non-bijective function is still considered a function because it still maps elements from one set to another. The only difference is that it is not a one-to-one correspondence, which is a property of bijective functions.
One example is the function f(x) = x^2, which maps all positive integers to positive integers, but also maps negative integers to positive integers. Another example is the function f(x) = 2x, which maps even integers to even integers, but odd integers to odd integers.
Non-bijective functions can be used in various mathematical and computer science applications, such as creating hash functions, generating pseudorandom numbers, and encoding data. They can also be used in cryptography for creating one-way functions that are difficult to reverse.