Dividing by zero

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I've never doubted that.

The real problem is to explain this so everyone can understand it, even those who lack mathematical education. Can you do that...?

Originally posted by FabianFnas
I've never doubted that.

The real problem is to explain this so everyone can understand it, even those who lack mathematical education. Can you do that...?

What is hard to understand about that proof? There will always be a number greater than 0 and less than 1 between any 'distinct real number'. Doesn't look that ominous to me🙂

Originally posted by sonhouse
What is hard to understand about that proof? There will always be a number greater than 0 and less than 1 between any 'distinct real number'. Doesn't look that ominous to me🙂

Well, if you can explain it without formulas, then you can explain it to anyone.
Of course, you can understand it, sonhouse, but could you make your mother to understand it? Or anyone else?

I gave lectures in astronomy to young people. I got highly respected alse by their teachers, because I could explain 'everything' without using any math at all.

Originally posted by FabianFnas
Well, if you can explain it without formulas, then you can explain it to anyone.
Of course, you can understand it, sonhouse, but could you make your mother to understand it? Or anyone else?

I gave lectures in astronomy to young people. I got highly respected alse by their teachers, because I could explain 'everything' without using any math at all.

Maybe you could say there is always a window of numbers greater than zero but less than one that will always be between any rational number?

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Thus making you a very bad teacher.

A good teacher is not a person who is an expert at a subject.

A good teacher is an expert at communicating the ideas in that subject to people who are
not experts in that subject, and who understand why people have a hard time understanding
some concepts.

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Well, I got what you were saying.

Originally posted by sonhouse
Maybe you could say there is always a window of numbers greater than zero but less than one that will always be between any rational number?

That's a good start. No deeper mathematic knowledge than this is needed to grasp the idea.

When I get a question from a child where children come from - I usually don't need biochemistry to tell him. I always level myself to the curious one before I answer any question. Ekonomics, astronomy, politics, whatever. No extras needed to show off. If he wants to know more, then I give him more.

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With his usual bias against me, Googlefudge has misunderstood what I wrote,

With your usual bias against me, you assume I misunderstand when I simply disagree.

And again, ffs, stop talking in third person. It's rude.

I mentioned the fact that I had made the
effort to learn a foreign language so I could understand mathematical books written in it.

Yes. I noticed the bragging. You do it allot.

Given that I found it
almost effortless to learn school mathematics, I naturally find it harder to understand
the learning difficulties of less gifted students. But that does not mean that I don't care.

And this is the point I was making.

Caring is [mostly] irrelevant. Understanding how and why people are having trouble grasping
a subject is crucial to being able to teach it well to anyone who is not themselves as gifted.
Every single 'teacher' I have met who never had any struggles of their own universally sucked
as a teacher. [based on the response of the entire class/other classes as opposed to my own
experience]

That you don't understand why others don't understand will almost guarantee that you will be
a bad teacher. Your attitude as evidence by your posts confirms it.

By the way, I never have heard a Chinese student--in contrast to some lazier Western
students--complain that it was too much work for them to learn mathematical notation.
A student has to memorize thousands of characters in order to read and write Chinese,
so memorizing some mathematical notation would be child's play in comparison.
Learning basic mathematical notation does not involve mastering mathematical concepts
except in the most rudimentary sense.

Who cares. Not relevant. And pure anecdote.

As I recall, Timothy Gowers (who has won a Fields Medal) has taken the position
(which I consider extreme) that effort means everything in succeeding in mathematics.
Reportedly, he likes to tell students that if they don't do as well as they wish in mathematics,
they should hold only themselves responsible for not having worked harder at it.
I don't know what he would tell a student who has spent every waking hour struggling with it.

And Timothy Gowers is wrong. His position isn't just 'extreme' it's incorrect.

Being good at something takes both ability and effort. The more ability [within limits] the less effort
required. For some, no amount of effort will suffice.

That he is brilliant at mathematics [and has also worked hard] has coloured his perceptions and
led him to believe that all it takes is effort because he takes his innate ability for granted and assumes
that everyone else has it too. [perhaps unconsciously, but nevertheless]

I am sure that for anyone not also brilliant [or at least very good] he is also a lousy teacher.

And in such a position as his, I suspect that he only gets brilliant pupils because those are the only
ones that make it through the filters to reach him.

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And you seem unable to grasp that the vast majority of people are not able [or willing]
to sit still [while being lectured at] long enough to learn the precise mathematical or
scientific language required to be able to understand the concept you are trying to
explain to them. So 'everyday language' is all you have, to try to get across the outline
of the concept and get them interested in it before boredom kicks in.

The best, and most popular 'educators' of science and mathematics get that.

You apparently don't.