Tag Archives: elements

The First Six Books of the Elements of Euclid, by Oliver Byrne (Taschen)

Posted on January 11, 2020 by Brent

Recently for my birthday I received a copy of Oliver Byrne’s 1847 edition of Euclid’s Elements (pictured at right), republished by Taschen Books in 2010. I’ve only just started reading it, but it’s beautiful and fascinating. Oliver Byrne was a … Continue reading →

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MaBloWriMo 19: groups from monoids

Posted on November 20, 2015 by Brent

So, you have a monoid, that is, a set with an associative binary operation that has an identity element. But not all elements have inverses, so it is not a group. Assuming you really want a group, what can you … Continue reading →

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MaBloWriMo 15: One more fact about element orders

Posted on November 16, 2015 by Brent

I almost forgot, but there is one more fact about the order of elements in a group that we will need. Suppose we have some and we happen to know that is the identity. What can we say about the … Continue reading →

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MaBloWriMo 14: Element orders are no greater than group size

Posted on November 15, 2015 by Brent

Today we will give an answer to the question: What is the relationship between the order of a group and the orders of its elements? Yesterday, I claimed we would prove that for any element of a group , it … Continue reading →

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MaBloWriMo 13: Elements of finite groups have an order

Posted on November 14, 2015 by Brent

Recall from yesterday that if is a group and is some element of the group, the order of is defined as the smallest number of copies of which combine to yield the identity element. I forgot to mention it yesterday, … Continue reading →

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