In this video I give some examples for "singular" or "discontinuous" limits and explain why it is important to know what they are. Corrections: The exponent at 1:45 should be 2 to the power of n, not 2 times n. The integral shown at 2:53 should have a "dt" at the end, not a "dx". At 4:53 that's not the dimension of the group, but the number of its elements. None of this is relevant to what I say, but sorry about those blunders anyway. Support me on Patreon: https://www.patreon.com/Sabine Michael Berry's essay is here: https://physicstoday.scitation.org/doi/abs/10.1063/1.1485555?journalCode=pto The proof that the integral series isn't constant is here: https://johncarlosbaez.wordpress.com/2018/09/20/patterns-that-eventually-fail/ Sound from ZapSplat.com #science #mathematics #education