Can anyone give me a good explanation of how and why words surjection and injection came into use in mathematical community? What do they exactly mean? Who introduced them?
I have a feeling students prefer names like ''one-to-one'' when they first learn about functions because it tells them about the property in a simple and direct way. It takes some time and use of ''injective'' and ''surjective'' to start feeling natural when you are a beginner!
On
Wikipedia says that "the terminology was originally coined by the Bourbaki group".
The reason for using special words is precision: "one-to-one" is ambiguous, for some it means "injection", for others it means "bijection".
This is all speculation, but...
The French "injectif" is a natural choice, since we are injecting one set into another. The French word "sur" means "on" (as in "on top of"), making "surjectif" a portmanteau of sorts. I suspect the prefix "bi" has the same meaning in French as in English, and so "bijectif" refers to functions having the two properties of injectivity and surjectivity.