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Moon Sighting vs Calculations

Regarding Calculations:

“Aadam narrated to us: Shu`bah narrated to us: al-Aswad ibn Qays narrated to us: Sa`eed ibn `Amr narrated to us: that he heard Ibn `Umar – radiyallaahu `anhumaa– report from the Prophet (Peace be upon him) that he said: <We are an unlettered nation, we do not write, nor do we reckon. The month is like this – and like this> – meaning once twenty-nine, and once thirty.”