Are there some differences so small that we cannot detect them? Are some quantities so similar (e.g., the number of spots on two speckled hens) that they simply look the same to us? Although modern psychophysical theories such as Signal Detection Theory would predict that, with enough trials, even minute differences would be perceptible at an above-chance rate, this prediction has rarely been empirically tested for any psychological dimension, and never for the domain of number perception. In an experiment with over 400 adults, we find that observers can distinguish which of two collections has more dots from a brief glance. Impressively, observers performed above chance on every numerical comparison tested, even when discriminating a comparison as difficult as 50 versus 51 dots. Thus, we present empirical evidence that numerical discrimination abilities, consistent with SDT, are remarkably fine-grained.