Tag Archives for math

Toronto space

In mathematics, in the realm of point-set topology, a Toronto space is a topological space that is homeomorphic to every proper subspace of the same cardinality.

There are five homeomorphism classes of countable Toronto spaces, namely: the discrete topology, the indiscrete topology, the cofinite topology and the upper and lower topologies on the natural numbers. The only countable Hausdorff Toronto space is the discrete space.[1]

The Toronto space problem asks for an uncountable Toronto Hausdorff space that is not discrete.[2]

https://en.wikipedia.org/wiki/Toronto_space

Zero is a non-multiple plural quantity in English

We say ‘one calorie’, or ‘two calories’, ‘three calories’, etc.

But we say ‘zero calories’ or ‘no calories’, as if it were a multiple like two, three, etc.

Yet if we say ‘not one calorie’, we say it thus, but ‘no calories’ thus.

 

We say there is one egg in the carton, or two eggs, or three eggs, or a dozen eggs.

Or if there are none left, we say there are zero eggs or no eggs – pluralized, as if zero were a multiple like two, three, or a dozen.

We will say ‘not a single egg was left’, but we’d say ‘no eggs were left’.

Why the Third-Pounder failed

Because ‘Murica!

One of the most vivid arithmetic failings displayed by Americans occurred in the early 1980s, when the A&W restaurant chain released a new hamburger to rival the McDonald’s Quarter Pounder. With a third-pound of beef, the A&W burger had more meat than the Quarter Pounder; in taste tests, customers preferred A&W’s burger. And it was less expensive. A lavish A&W television and radio marketing campaign cited these benefits. Yet instead of leaping at the great value, customers snubbed it.

Only when the company held customer focus groups did it become clear why. The Third Pounder presented the American public with a test in fractions. And we failed. Misunderstanding the value of one-third, customers believed they were being overcharged. Why, they asked the researchers, should they pay the same amount for a third of a pound of meat as they did for a quarter-pound of meat at McDonald’s. The “4” in “¼,” larger than the “3” in “⅓,” led them astray.

MPAI…