What is a bijective function?
Q: What is a bijective function?
A: A bijective function, also known as a bijection, is a mathematical function that is both an injection and a surjection.
Q: What does it mean for a function to be an injection?
A: An injection means that for any two elements a and a' in the domain A, if f(a)=f(a'), then a=a'.
Q: What does it mean for a function to be a surjection?
A: A surjection means that for every element b in the codomain B, there is at least one element a in the domain A such that f(a)=b.
Q: What is the equivalent statement for a bijection?
A: The equivalent statement for a bijection is that for every element b in the codomain B, there is exactly one element a in the domain A such that f(a)=b.
Q: What is another name for bijection?
A: Bijection is also known as "1-1 correspondence" or "one-to-one correspondence".
Q: Who introduced the terms bijection, surjection, and injection?
A: The terms bijection, surjection, and injection were introduced by Nicolas Bourbaki and a group of other mathematicians in the 1930s.
Q: What did Bourbaki and other mathematicians publish in the 1930s?
A: Bourbaki and other mathematicians published a series of books on modern advanced mathematics.
