Groups and Vector Spaces
If the component sets are ordered groups then the result is a non-Archimedean group, because e.g. n(0,1) < (1,0) for all n.
If the component sets are ordered vector spaces over R (in particular just R), then the result is also an ordered vector space.
Read more about this topic: Lexicographical Order
Famous quotes containing the words groups and/or spaces:
“In properly organized groups no faith is required; what is required is simply a little trust and even that only for a little while, for the sooner a man begins to verify all he hears the better it is for him.”
—George Gurdjieff (c. 1877–1949)
“When I consider the short duration of my life, swallowed up in the eternity before and after, the little space which I fill and even can see, engulfed in the infinite immensity of spaces of which I am ignorant and which know me not, I am frightened and am astonished at being here rather than there. For there is no reason why here rather than there, why now rather than then.”
—Blaise Pascal (1623–1662)