MATHS BITE: The Cantor Set

And they call them “real” numbers!

mathsbyagirl

The Cantor Set is constructed in the following way:

Start with the interval [0,1]. Next, remove the open middle third interval, which gives you two line segments [0,1/3] and [2/3,1]. Again, remove the middle third for each remaining interval, which leaves you now with 4 intervals. Repeat this final step ad infinitum.

The points in [0,1] that do not eventually get removed in the procedure form the Cantor set.

How many points are there in the Cantor Set?

Consider the diagram below:

An interval from each step has been coloured in red, and each red interval (apart from the top one) lies underneath another red interval. This nested sequence shrinks down to a point, which is contained in every one of the red intervals, and hence is a member of the Cantor set. In fact, each point in the Cantor set corresponds to a unique infinite sequence of nested intervals.

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“Digital”, the new buzword

Now for more exiting and less mathematical stuff.

I don’t know if this is “the way forward” or “just bullshit”, but McKinsey knows (something).

So on with “Digital” in education:

This is the introduction –

Companies today are rushing headlong to become more digital. But what does digital really mean?

For some executives, it’s about technology. For others, digital is a new way of engaging with customers. And for others still, it represents an entirely new way of doing business. None of these definitions is necessarily incorrect. But such diverse perspectives often trip up leadership teams because they reflect a lack of alignment and common vision about where the business needs to go. This often results in piecemeal initiatives or misguided efforts that lead to missed opportunities, sluggish performance, or false starts.

And the rest of it is here

http://www.mckinsey.com/industries/high-tech/our-insights/what-digital-really-means

Have fun. The words are easy.

 

 

 

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