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20 June, 2010 in Set Theory. It’s been a little while since I last posted here, mostly due to laziness. However, I find myself a little rich with time at the moment, so I will try to pick up where I left off. In the last post, Heath left a comment pointing out that I may have been a little hasty, and that not properly introducing the Cantor set. First, we recall a little background. An interval. Of real numbers is a set of numbers with the property that if two numbers lie in. An open interval,. If the na...

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20 June, 2010 in Set Theory. It’s been a little while since I last posted here, mostly due to laziness. However, I find myself a little rich with time at the moment, so I will try to pick up where I left off. In the last post, Heath left a comment pointing out that I may have been a little hasty, and that not properly introducing the Cantor set. First, we recall a little background. An interval. Of real numbers is a set of numbers with the property that if two numbers lie in. An open interval,. If the na...

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Expand and Simplify | sdnj.wordpress.com Reviews

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20 June, 2010 in Set Theory. It’s been a little while since I last posted here, mostly due to laziness. However, I find myself a little rich with time at the moment, so I will try to pick up where I left off. In the last post, Heath left a comment pointing out that I may have been a little hasty, and that not properly introducing the Cantor set. First, we recall a little background. An interval. Of real numbers is a set of numbers with the property that if two numbers lie in. An open interval,. If the na...

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About the blog. | Expand and Simplify

https://sdnj.wordpress.com/about

I started this blog for two main reasons, which I outline in my first post, but shall rehash here:. 2 As a place to sometimes write about my current areas of interest or research, and the reading I’m doing in support of these. These posts will always be marked, and may often contain errors, an unavoidable part of the learning process, but as someone wise once said: “You seldom learn from success.” Feel free to read these, and even provide comments and constructive criticism. Comments feed for this article.

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A brief diversion. | Expand and Simplify

https://sdnj.wordpress.com/2010/06/20/a-brief-diversion

20 June, 2010 in Set Theory. It’s been a little while since I last posted here, mostly due to laziness. However, I find myself a little rich with time at the moment, so I will try to pick up where I left off. In the last post, Heath left a comment pointing out that I may have been a little hasty, and that not properly introducing the Cantor set. First, we recall a little background. An interval. Of real numbers is a set of numbers with the property that if two numbers lie in. An open interval,. If the na...

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Kissing Cantor 1 | Expand and Simplify

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10 February, 2010 in Set Theory. As mentioned in the previous post, I would like show the proof a very small part of the construction of a space filling curve. The part I wish to talk about is the third line of the construction here. Which starts with “Since the Cantor set…”. While I will not give a complete proof of the homeomorphism. I will show the bijection, and not the bi-continuity, as this is more likely to confuse the intended audience than make anything clear. Are bijective functions: all points...

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First Post! | Expand and Simplify

https://sdnj.wordpress.com/2010/01/10/first-post

10 January, 2010 in Topology. Welcome to the first post of my new blog,. And those outside, for planting the idea in my head (one can’t help but think that they, too, have improved since their earlier posts). The first thing I’d like to talk about is the really neat phenomenon of Peano curves, or space-filling curves. Behaving like a Hilbert curve, which is a kind of space-filling curve. I thought I’d get around to starting this blog. Is topologically equivalent (homeomorphic) to the cartesian product.

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20 June, 2010 in Set Theory. It’s been a little while since I last posted here, mostly due to laziness. However, I find myself a little rich with time at the moment, so I will try to pick up where I left off. In the last post, Heath left a comment pointing out that I may have been a little hasty, and that not properly introducing the Cantor set. First, we recall a little background. An interval. Of real numbers is a set of numbers with the property that if two numbers lie in. An open interval,. If the na...

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