markusblazer
14.02.2020 •
Mathematics
Let -? and ? denote two distinct objects, neither of which is in R. Define an addition and scalar multiplication on R U {?} U {-?} as you could guess from the notation. Specifically, the sum and product of two real numbers is as usual, and for t ? R define
t? = { -? if t<0 , 0 if t=0, ? if t>0
t(-?) = { ? if t<0, 0 if t=0, -? if t>0
t+? = ?+t=?, t+(-?)=(-?)+t=-?, ?+?=?, (-?)+(-?)=-?, ?+(-?)=0
IsR U {?} U {-?} a vector space over R? Please Explain.
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