## I am in Japan, no internet connection yet

To all my readers.  I just moved to Japan for a 1.5-year study grant. I have no internet access until October 8 due to some paper works to be done, so I will not be able to update my blogs.

Anyway, I have a lot of math stuff in mind to write later, so please be patient.

Arigato gozaimasu (Thank you.)

## The Number of Points on Two Line Segments

We say that a set is countably infinite if we can pair the elements with set of counting numbers 1, 2, 3, and so on. Believe it or not, the number of positive integers and the number of integers (both negative and positive including 0) have the same number of elements. It is because we can pair them in a one-to-one correspondence such as shown in the below.

As shown on the table, if we continue indefinitely, we know that we can pair each counting number with an integer in a one-to-one correspondence without missing any element.

Using this concept, we show intuitively that the number of points on two line segments is equal even if they have different lengths. We can do this by showing that for each point on segment $\overline{AB}$, there is a corresponding point on segment $\overline{CD}$. » Read more

## GeoGebra App for iPad, Now Available

Last week, GeoGebra has announced the released of the GeoGebra tablet app versions. The versions were only available in Android and Windows 8.

Now, the GeoGebra App for iPad is already available for download. More than 50 GeoGebra tutorials on using the software can be read at the Math and Multimedia GeoGebra page if you are interested to learn. If you want to view the capabilities of GeoGebra, more than 40 thousand applets can also be found at GeoGebraTube.

GeoGebra (www.geogebra.org) is free dynamic mathematics software for all levels of education that brings together geometry, algebra, spreadsheets, graphing, statistics and calculus in one easy-to-use package. Interactive learning, teaching and evaluation resources created with GeoGebra can be shared and used by everyone at www.geogebratube.org

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