Soul mate.

Historical usage of the concept:
1) Plato
In his dialogue The Symposium, Plato has Aristophanes present a story about soulmates. Aristophanes states that humans originally had four arms, four legs, and a single head made of two faces, but Zeus feared their power and split them all in half, condemning them to spend their lives searching for the other half to complete them.

2) Theosophy
According to Theosophy, whose claims were modified by Edgar Cayce, God created androgynous souls—equally male and female. Later theories postulate that the souls split into separate genders, perhaps because they incurred karma while playing around on the Earth, or "separation from God." Over a number of reincarnations, each half seeks the other. When all karmic debt is purged, the two will fuse back together and return to the ultimate.

Current usage of the concept:
In current usage, "soulmate" usually refers to a romantic partner, with the implication of an exclusive life-long bond.

Would I really want to be with someone who doesn't think I'm his soul mate?