Show-by-use-of-the-characteristics-of-a-vector-space-that-the-set-x-R-with-the-following-operations-and-builds-a-vector-space-Use-vector-space-axioms-x-y-be-x-y-for-R

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Question Number 1537 by 2closedStringsMeet last updated on 17/Aug/15

$$Showbyuseofthecharacteristicsof$$$$avector-space,thattheset\overrightarrow{x}\in {\mathbb{R}}_{+}$$$$\mathrm{with}\mathrm{the}\mathrm{following}\mathrm{operations}\oplus and$$$$buildsavector-space.$$$$\ast Usevector-spaceaxioms$$$$\ast \overrightarrow{x}\oplus \overrightarrow{y}be\overrightarrow{x}\cdot \overrightarrow{y}$$$$\ast for\lambda \in \mathbb{R}set\lambda \overrightarrow{x}equal\stackrel{\to \lambda }{x}$$

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