# Tag Archives: unlearning

## Operators, Functions, and Properties – part 30

In many of the posts in this series we’ve shown operators that work on a single number coming in and that produce a single number coming out.  This is a hugely important subcategory of operators, but single-in single-out operators aren’t … Continue reading

## Representations – Black Boxes – Equivalence 2

We ended the previous post in this series by looking at this figure: To recap, a black box is something where we have access to the behavior but not the internal organization.  We can propose a model for a black … Continue reading

## Operators, Functions, and Properties – part 1

I intend to write some things on operators in mathematics, beginning in this post.  Functions and properties will be brought in as appropriate.   The idea of operators is absolutely basic and central to computers and computing; they are also important … Continue reading

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## Representations – Black Boxes – Equivalence

I introduced the notion of a black box in an earlier post as some thing that has an internal organization that drives its behavior, and though we can see the behavior, we don’t have perfect knowledge of that internal organization.  … Continue reading

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## Representations – Number and Some Alternatives

There are lots of ways to represent number – such as the number “ten”.  As grown-ups, we’re so used to a particular way of representing “ten” that we don’t often stop to think about what we’re doing – we just … Continue reading

## Representations – Formulas and Some Alternatives

There are systems of notation for mathematical expressions that are in wide use.  One of them is so widely used and so well-known that we often think of it as the only one, the real one, the true one and … Continue reading

## Key Math Ideas Not Taught In School – Invariants

“Counting” involves a number of different mathematical ideas If you watch really young children count, you may notice that they aren’t all doing the same thing.  For some children, counting “one-two-three” is done in very much the same way as … Continue reading

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## Key Math Ideas Not Taught In School

There is a shape, a progression, to the typical school curriculum from Kindergarten through High School, at least in the United States, and this progression hasn’t changed much in the last 50 years or so.  We’ve gotten used to this … Continue reading

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## Quantity – Different Kinds of Numbers: Notations

When you think of operations as having a front office component and a back office component, where the front office component provides the public face and the back office component provides the implementation, as we first introduced in the post … Continue reading

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## Quantity – Different Kinds of Numbers: Classes

Let me recap what this series of blog posts has been about.  I’ve been looking at different kinds of quantities, different kinds of numbers.  I started with observations like: it’s meaningless to add 1951 AD to 2009 AD but completely … Continue reading

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