How to say the set of real numbers is closed under addition. in Japanese

1)実数実数(jissuu) (n,adj-no) real numberの(no) (prt) indicates possessive/nominalizes verbs and adjectives/substitutes for "ga" in subordinate phrases/indicates a confident conclusion/ indicates emotional emphasis/indicates question集合集合(shuugou) (n,vs,adj-no) gathering/assembly/meeting/setは(ha) (int) indicating a subject/yes/indeed/well/ha!/what?/huh?/sigh加法加法(kahou) (n) additionについてについて(nitsuite) (exp) concerning/regarding/per/for every閉じno dictionary result, likely a conjigated verbno dictionary result, likely a conjigated verbているている(teiru) (v) an "ing" form of the previous verb。(。) Japanese period "."    
jissuu no shuugou ha kahou nitsuite toji teiru 。
Grammer form日常会話 (Casual form)Casual form (nichijoukaiwa)
everyday casual language, commonly used between friends and family.
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Translation by thyc244
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