The study of limits asks, where does this quotient go if I allow myself to take increasingly larger values for x? That is, if I let x be 0, then 10, then 100, and 1000, and so on, I get:
So what you're probably noticing is that this fraction gets closer and closer to 1. Indeed, when I take increasingly larger values for x, whether I add 20 or 30 really makes no difference, since x is so big. In a more familiar context, if you have 1 billion dollars and I give you 20 more, that's more or less the same to you as if I give you 30 more -- you're already so stacked.
In the biz, we express this very formally by saying the following:
So we start with 20 and 30, which are distinctly different numbers, and eventually limit to 1, so it looks like x+20 and x+30 are eventually the same thing. In other words, 20 is the new 30, a statement which formed the anti-thesis of a delightful recent TED talk by Clinical Psychologist Meg Jay.
Being that I am in my 20s, and dancing dangerously on the edge of my 30s, this spoke to me. Jay clams that although we've pushed back the traditional 20-something roles -- marriage, childbirth -- into our 30-somethings, the 20s have not become the "lost decade." Although we may exit them just as single and childless as we entered them, our 20s are still the point in our lives when we learn how to be husbands, wives, parents, and good citizens.
I spend a lot of time thinking about how crazy the idea of kids sounds to me, or how I can't imagine why I'd ever be anybody's wife, but it's nice to think that the life skills I'm learning right now are indeed equipping me for the job. It's also nice that for one fleeting moment, somebody has acknowledged the millenials as more than just a pack of emotionally stunted dreamers.
So I say dream on dreamers, but dream with the knowledge that one day as x gets very very large, all of this will come in handy.
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