The debate goes beyond that point, as illustrated by the lengthy Wikipedia section:

https://en.wikipedia.org/wiki/0%5E0#Zero_to_the_power_of_zer...

From an undergraduate math point of view, it's wise to understand that 0^0 is not well defined.

This argument assumes that the function f(x,y)=x^y is continuous near 0 and therefore lim (f(x)^g(x)) = (lim f(x))^(lim g(x)) at zero. But since it's not continous, that formula does not necessarily hold true.

I also have had many migraines with visual aura, and have exactly one similar experience of perceptual blindness.

I don't want to give a medical diagnosis, but this sounds familiar to me as a migraine sufferer.

You might be experiencing a migraine without headache: https://en.wikipedia.org/wiki/Acephalgic_migraine

Since there are still ~200 countries without a Fields Medal, this isn't mathematically remarkable in comparison to the parent point.

So, I understand instead that you're identifying this as notable for the following reason:

There are 100 times more women in the world than Canadians, yet women and Canadians have the same number of Fields Medals.

First of all, there's not enough data to be statistically significant in any of my ramblings, so it's all kind of hand-wavy and I apologize for that.

But my general feeling is that there used to be a few "powerhouse" countries and institutions that dominated, but that has been changing for many years. There's a lot more diversity these days. So I think kiyoto's point speaks to the changes there.

In 1950, it would have been pretty inconceivable that a woman from Iran would have had the access and opportunities to contribute to mathematics in a way that would have earned a Fields medal; in 2014, it's a first-time feat; hopefully, in the future, it quickly becomes mundane.

"not enough data to be statistically significant"

^suspect this is incorrect.

> Oh dear. When a student answers that 7/12 is 1.5 and doesn't immediately see why this couldn't possibly be true you know that the problem is rote learning of algorithms.

Not really, no.

1. Students have to have a good concept of division, as you suggest.

2. Students have to know a method of division that accurately gets a precise answer. (whether this is via an algorithmic method or via a calculator)

3. Students have to know that their answer to (2) should correspond to their concept in (1)

4. Students have to recognise that they can check their answer using (3), and then remember to actually check this.

A good teacher will teach all four parts of this process. However, it's not possible to teach part 4 without first teaching parts 1 and 2. Every single child makes this same mistake at some point in their learning. This is not really a "problem" and it doesn't indicate a failure of teaching - in fact, the opposite here: the important thing is that the teacher has identified it and can advise the child on how to improve their understanding.

That's what teaching is. As you say, many adults have not consistently achieved part 4 - in fact, it's not immediate at all: it has to be learned.

So the reason for working longer hours is to ensure that the Chinese people have to work longer hours (which ensures that Westerners have to work longer hours)?

Seems like a pretty bad prisoner's dilemma - and a pointless exercise if you already accept that China will ultimately win.