Archive for January 16th, 2018

January 16, 2018

Quote of the day

by Neil Rickert

From a post on Frank Schaeffer’s blog:

White evangelicals take note: If Trump is president because of “God’s will,” then your God must be a white trash, philandering, money-laundering, Putin-stooge, hate-filled, racist liar, too.

Well, no, I am not planning to have a daily “quote of the day” feature.  But this stood out as worth repeating.

January 16, 2018

Generalization in mathematics

by Neil Rickert

Generalization is an important part of mathematics, and I shall discuss that here.  My discussion will mostly consist of examples with commentary on those examples.

I’m planning a future post on generalization in science.

Numbers

The simplest example has to do with numbers.  And our use of numbers presumably started with counting.  By assigning names, from a fixed sequence (1,2,3, …), we could count objects.  And then we could compare the results from counts of different collections of objects. This turned out to be useful for keeping track of quantities.

Rules were developed to deal with counting of groups of objects.  If we knew the counts of each of two groups, we could combine those with addition rules, to get the combined count.  And if we has several groups of the same count, we could combine those with multiplication rules.

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