Dear Noble,
I wish you all the best in your endeavour to rid the world of oxymorons, misnomers and other aberrations and abuses of the English language.
In this you may wish to take into account that a ‘function’ is not always a 1-to-1 mapping, as an example the square root function springs to mind.
Quoting is indeed hazardous. In the linked document you can see the ‘R’ actually represents the set of real numbers (the mathematical notation got lost in the copy-paste, my apologies for this). Being a non-native speaker whose grasp of correct usage is far below yours, mapping ‘into’ a set did not strike me as an offense. Thank you for pointing out my error in this.
Have a good life,
Tom