"one to one" as injective and "onto" as surjective

[onlyReferee]

Have you ever met these notations wrt to functions, isomorphisms, etc Do you think they should be preferred instead of the corresponding longer versions

[j18eos]

"onlyReferee":Thank you for your reply, j18eos ...

Not at all.

"onlyReferee":It seems that these last ones are more familiar for our Italian people, is not it

I don't believe; durign the lessons and the seminars, I saw write and I listened say "onto" instead "surjective" and viceversa and the same for the other verbal expression.

[DavideGenova1]

The longer forms also are more elegant, to the ear of native English speakers too. "Two-way" and "one to one" sound quite informal.

[onlyReferee]

Thank you for your reply, j18eos
Since the topic is about these notations what about the short one for "two-way" instead of "bijective" Also in this case my professor who is following me with thesis suggests me to use the longer notation.
It seems that these last ones are more familiar for our Italian people, is not it

[j18eos]

"onlyReferee":Have you ever met these notations wrt to functions, isomorphisms, etc ...

Yes, I have!

"onlyReferee":...Do you think they should be preferred instead of the corresponding longer versions

Imho, it's indifferent! When I write, I prefer the longer version; when I speak, it's possible that I use the shorter version.