taken from Tafsir Ibn Kathir.
The meaning of Ar-Rahman Ar-Rahim.
Ar-Rahman and Ar-Rahim are two names derived from Ar-Rahman (the Mercy), but Rahman has more meanings that pertain to mercy than Ar-Rahim...
...Al-Qurtubi said, "It was said that both Ar-Rahman and Ar-Rahim have the same meaning, such as the words Nadman and Nadim, as Abu 'Ubayda has stated. Abu 'Ali Al-Farsi said 'Ar-Rahman, which is exclusively for Allah, is a name that encompasses every type of mercy that Allah has. Ar Rahim is what effects the believers, for Allah said,
And He is ever Rahim (merciful) to the believers. 33:43
Also ibn 'Abbas said -about Ar-Rahman and Ar-Rahim, they are two soft names, one of them is softer than the other (meaning it carries more implications of mercy).
Ibn Jarir said: As-Surri bin Yahya At-Tamimi narrated to me that 'Uthman bin Zufar related that Al-'Azrami said about Ar-Rahman and Ar-Rahim, "He is Ar-Rahman with all creation and Ar-Rahim with the believers." hence Allah's statements,
Then He rose over (Istawa) the Throne (in a manner that suits His majesty), Ar-Rahman.25:59 and,
Ar-Rahman (Allah) rose over (Istawa) the (Mighty) Throne (in a manner that suits His Majesty). 20:5.
Allah thus mentioned the Istawa- rising over the Throne along with His name Ar-Rahman, to indicate that His mercy encompasses all of His creations. Allah also said,
And He is ever Rahim (merciful) to the believers. Thus encompassing the believers with His Name Ar-Rahim. They said, "this testifies to the fact that Ar-Rahman carries a broader scope of meanings pertaining to the mercy of Allah with His creation in both lives. Meanwhile, Ar-Rahim is exclusively for the believers."
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