We report the first results of AS2UDS: an 870 $mu$m continuum survey with the Atacama Large Millimeter/Submillimeter Array (ALMA) of a total area of $sim$ 50 arcmin$^2$ comprising a complete sample of 716 submillimeter sources drawn from the SCUBA-2 Cosmology Legacy Survey (S2CLS) map of the UKIDSS/UDS field. The S2CLS parent sample covers a 0.96 degree$^2$ field at $sigma_{850}=0.90pm0.05$ mJy beam$^{-1}$. Our deep, high-resolution ALMA observations with $sigma_{rm 870}sim$ 0.25 mJy and a 0.15--0.30 FWHM synthesized beam, provide precise locations for 695 submillimetre galaxies (SMGs) responsible for the submillimeter emission corresponding to 606 sources in the low resolution, single-dish map. We measure the number counts of SMGs brighter than $S_{rm 870}geq$ 4 mJy, free from the effects of blending and show that the normalisation of the counts falls by 28 $pm$ 2% in comparison to the SCUBA-2 parent sample, but that the shape remains unchanged. We determine that 44$^{+16}_{-14}$% of the brighter single-dish sources with $S_{850}geq$ 9 mJy consist of a blend of two or more ALMA-detectable SMGs brighter than $S_{870}sim$ 1 mJy (corresponding to a galaxy with a total-infrared luminosity of $L_{IR}geq$ 10$^{12}$ L$_odot$), in comparison to 28 $pm$ 2% for the single-dish sources at $S_{rm 850}geq$ 5 mJy. Using the 46 single-dish submillimeter sources that contain two or more ALMA-detected SMGs with photometric redshifts, we show that there is a significant statistical excess of pairs of SMGs with similar redshifts ($<$1% probability of occurring by chance), suggesting that at least 30% of these blends arise from physically associated pairs of SMGs.
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