The Math Myth

Post by Davidp00 » Sat, Sep 03, 2016, 2:47 PM UTC

js8 wrote: post #13

I can tell from personal experience that I only properly understood simpler mathematics when I started learning more complicated one. For instance, in linear algebra, finite dimensional (euclidean) vector spaces became a cakewalk once we started talking about functional analysis. So, I think, even if you don't need that particular stuff in your work, it's still a good training. Also, there has been a pushback against…

Post by kazinator » Sat, Sep 03, 2016, 2:53 PM UTC

iopq wrote: post #48

sp527 wrote: post #44

Earlier quoted context omitted.

Hardly. We use this reduction because it's essential from a mathematical and axiomatic perspective and because limits are a fundamental construct. But more philosophically, a natural and nonterminating simulation of 0.999... (were it possible) would never strictly equal 1. You would wait an infinite amount of time for it to do so. This comes down to how you view the problem. I would never argue with this through the…

It's not a reduction. If you try to find where to put 0.999... on the number line, it has to go exactly where 1 is. For one thing, 1 - 0.999... = 0.000... because you never get to have any remainder since 0.999... is infinite. Or here's another proof: x = 0.999... 10x = 9.999... 10x - x = 9.999... - 0.999... 9x = 9.000... = 9 9x = 9 x = 1

Post by alejohausner » Sat, Sep 03, 2016, 2:56 PM UTC

soVeryTired wrote: post #70

rntz wrote: post #51

Earlier quoted context omitted.

You don't need to understand anything about infinitesimals to understand 0.999... = 1. Perhaps you meant limits? The "standard" approach would be to point out that Σ_{i=1}^∞ 9/(10^i) = 1 (that is, the sum from i = 1 to infinity of 9/(10^i) is 1), and understanding an infinite summation requires the concept of a limit. (Of course, there are simpler proofs that use only basic algebra and intuition about decimals; a lim…

Limits use a construction that's pretty similar to an infinitesimal. The epsilon-delta definition of a limit is no joke for students.

Post by kozikow » Sat, Sep 03, 2016, 3:00 PM UTC

yodsanklai wrote: post #67

sp527 wrote: post #19

This has so much more to do with the lack of easily monetizable applications of complex mathematics. I'm sure a significant number of engineers and STEM professionals feel (as I do) that they're deliberately eschewing those subjects not for a lack of interest, but rather as a response to market demand. The market of people who are genuinely passionate about complex subjects in math and science is saturated relative t…

> It makes more sense for an intelligent person to take the lower overhead and more achievable approach to becoming a value creator (e.g. full stack engineer with a strong focus on product development) I would say that the surest way to make money for a mathematicaly-inclined person is to graduate in maths from a prestigious school and work in finance. At least, that's how I feel when I look at alumni from my school.…

Post by mikebelanger » Sat, Sep 03, 2016, 3:06 PM UTC

jdietrich wrote: post #80

majos wrote: post #53

I think one non-obvious benefit of a good mathematics education is that you have little choice but to develop a tolerance for and understanding of being wrong. See Jeremy Kun's blog post [1] for more, but my own experience has been that in e.g. discussing different ways to solve a problem or prove something almost every person eventually has an "oh, no, I see, I'm wrong and you're right" moment. Not that every mathem…

In my experience, a surprising number of people with a humanities education simply don't believe in "wrongness", but merely differences of opinion. They regard truth as peculiar abstraction used by mathematicians and hard scientists, not a phenomenon that actually exists. It's hard for someone to admit to being wrong if they don't even believe in the concept.