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A rational number is any number that can be written as a ratio of two integers (hence the name!). In other words, a number is rational if we can write it as a fraction where the numerator and denominator are both integers. The term "rational" comes from the word "ratio," because the rational numbers are the ones that can be written in the ratio form p/q where p and q are integers. Irrational, then, just means all the numbers that aren't rational. Every integer is a rational number, since each integer n can be written in the form n/1. For example 5 = 5/1 and thus 5 is a rational number. However, numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers. So the set of all rational numbers will contain the numbers 4/5, -8, 1.75 (which is 7/4), -97/3, and so on. Is .999 repeating a rational number? Well, a number is rational if it can be written as A/B (A over B): .3 = 3/10 and .55555..... = 5/9, so these are both rational numbers. Now look at .99999999..... which is equal to 9/9 = 1. We have just written down 1 and .9999999 in the form A/B where A and B are both 9, so 1 and .9999999 are both rational numbers. In fact all repeating decimals like .575757575757... , all integers like 46, and all finite decimals like .472 are rational.

This is an important speech on a very important subject. But before I begin, I want to just speak briefly about Haiti, because during the last eight days, the people of Haiti and the people of the world have joined together to deal with a tragedy of staggering proportions. Our hemisphere has seen its share of hardship, but there are few precedents for the situation we’re facing in Port-au-Prince. Communication networks have played a critical role in our response. They were, of course, decimated and in many places totally destroyed. And in the hours after the quake, we worked with partners in the private sector; first, to set up the text “HAITI” campaign so that mobile phone users in the United States could donate to relief efforts via text messages. That initiative has been a showcase for the generosity of the American people, and thus far, it’s raised over $25 million for recovery efforts.

Information networks have also played a critical role on the ground. When I was with President Preval in Port-au-Prince on Saturday, one of his top priorities was to try to get communication up and going. The government couldn’t talk to each other, what was left of it, and NGOs, our civilian leadership, our military leadership were severely impacted. The technology community has set up interactive maps to help us identify needs and target resources. And on Monday, a seven-year-old girl and two women were pulled from the rubble of a collapsed supermarket by an American search-and-rescue team after they sent a text message calling for help. Now, these examples are manifestations of a much broader phenomenon.

The spread of information networks is forming a new nervous system for our planet. When something happens in Haiti or Hunan, the rest of us learn about it in real time – from real people. And we can respond in real time as well. Americans eager to help in the aftermath of a disaster and the girl trapped in the supermarket are connected in ways that were not even imagined a year ago, even a generation ago. That same principle applies to almost all of humanity today. As we sit here, any of you – or maybe more likely, any of our children – can take out the tools that many carry every day and transmit this discussion to billions across the world.