Irrational Numbers as Decimals

Introduction

In Rational and Irrational Numbers post, we have discussed that  \sqrt{2} is irrational.  Aside from its radical form,  using a calculator or a computer, we can approximate its value; for example, \sqrt{2} \approx 1.414213562. As we can see, irrational numbers can also be represented as decimals. The more powerful the computer, the more accurate we can approximate.

Some Definitions

Decimal numbers with finite number of digits are called terminating decimals, while decimals with infinite number of digits are called non-terminating decimals. The number 0.345 is a terminating decimal, while 0.999 \cdots is a non-terminating decimal. The \cdots symbol means that the 9s extend indefinitely.

Decimals with repeating digits; that is, the digits that repeat infinitely are called repeating decimals. The numbers 0.999 \cdots0.4545 \cdots,  and 5.144144144 \cdots are repeating decimals. » Read more

Gmail asking for password — be careful!

When I opened my email this morning, I received an ‘Identity Verification’ email from ‘Gmail’ (verifiesences@gmail.com), which I think is a hoax.

The content of this letter is the following.

We have received several complaints from users unable to gain access to their email account, as a result of that, we are upgrading our security systems and making sure each user account is not accessed unauthorised. We do not want you to loose access to your Account since your login information are no longer valid on our database system. Now, the Gmail Account Team need to confirm your profile details below for verification purpose and to confirm that you own this Account:


*Username:
*Pasword:
*Date of Birth:
*Country:

Please answer each question as thoroughly and accurately as possible, Your detailed answers will help us ensure that only you get access to your account. In an effort to protect your privacy and keep your information secure, if we detect unusual activity on the account, we may disable it.

Thank you for using our email service!

I am pretty sure that this email is not from Gmail, so do not reply to this email. As a general rule, DO NOT GIVE YOUR PASSWORD to anyone via email or any electronic form.

 

What are RSS Feeds?

Introduction

When you are reading a book, you use a bookmark to mark a page where you stopped or a page which is important to you. This also happens on the web. You probably have an list of  the URLs of websites you like. Some of you are probably familiar with the bookmark feature of your browsers: the star in Google Chrome’s address bar, the Favorite>Add to Favorites in Internet Explorer, and CLTR+D in Firefox.

Browser bookmarking is good way to mark your favorite sites, but the problem is that browsers are not capable of informing you when site you bookmarked new articles or updates.  You have to visit the website to check for new articles.

This is where RSS comes in.  It’s like a browser saying ‘Hey, Math and Multimedia has a new post.’ This is similar to email subscriptions: users are informed whenever a site is updated.  Some RSS feed management providers such as Feedburner offer RSS email subscriptions as well. » Read more

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