What is a one-to-one correspondence or one to one mapping? I have heard the later term used plenty of times in linear algebra classes I've taken, i.e. there is a one to one mapping from a subspace to another. But I've never really understood what that meant entirely. Are the two above phrasees the same, or different? And if they are different how are they different? Quick sidenote: this is not homework of any kind, no problems/grades or any such thing. I do self study in my down time when I'm not in school, and this came up in a math book I'm looking at and I think I need to fully understand what it means so I get the full understanding and not just a superficial understanding that I can confuse for real understanding. Thanks for your time and any answer!