The subject you discussed is whether "a" singularity can exist. The answer is no. A singularity is a mathematical phenomenon that indicates that the physics has broken down and that we need better theory. There's no actual singularity inside a black hole, a zero-dimensional point of infinite mass or whatever. That's a mathematical anomaly that doesn't exist in reality.
"The" singularity is the idea that computers will become smarter than us and we'll upload our minds and all that kind of fashionable nonsense. Completely separate idea from what you are discussing.
But what do I know, I've never even given a TED talk. Come the singularity I'll be consigned to the fossil museum along with my buggy whip.The technological singularity—also, simply, the singularity—is a hypothetical point in time at which technological growth becomes uncontrollable and irreversible, resulting in unforeseeable changes to human civilization. According to the most popular version of the singularity hypothesis, called intelligence explosion, an upgradable intelligent agent will eventually enter a "runaway reaction" of self-improvement cycles, each new and more intelligent generation appearing more and more rapidly, causing an "explosion" in intelligence and resulting in a powerful superintelligence that qualitatively far surpasses all human intelligence.