The real line runs from negative to positive infinity and consists of rational and irrational numbers. It generally appears horizontally, and every point corresponds to a real number. Also known as a number line in school, the real line is said to be one of the most useful ways to understand basic mathematics. Wolfram|Alpha can now aid you in learning the difference between x<-5 and x>5, or Abs[x]<2.

Wolfram|Alpha now graphs inequalities and points on the real line. This new feature in Wolfram|Alpha allows you to plot a single inequality or a list of multiple inequalities. Let’s start off simply and try “number line x<100”.

Number line x<100

You can easily see that this is the set of all real numbers from negative infinity to, but not including, 100.

What if you need to plot a more difficult inequality, like “number line 3x<7x^2+2”? This plot will show that the solutions to this inequality are all real numbers between negative and positive infinity.

number line 3x<7x^2+2

Or try “-1<sin(x)<=1”:

-1 <sin(x)<=1

Of course, Wolfram|Alpha can also plot a list of numbers on a number line. Try something like “e, Pi, 5, square root of 2”.

e, Pi, 5, square root of 2

This will nicely depict these values on the real line.

What if you want to plot more than one inequality? Just give Wolfram|Alpha a list, for example, “x<2, x>5x+7, x=10, x>=-2x”.

x<2, x>5x+7, x=10, x>=-2x

Wolfram|Alpha now has the ability to plot 1D, 2D, and 3D graphics, so be sure to use it for all of your graphical needs!

3 Comments

Interesting idea, but wouldn’t it make sense to graph “steps” on the number line as arrows, so in other words “3-4″ would give an arrow from 4 to 3?
And secondly shouldn’t the number line include imaginary values as well for the sake of completeness, although I don’t think it will serve that much of a purpose.

Posted by David Mulder January 10, 2011 at 10:27 am Reply

Hello David,

Wolfram|Alpha doesn’t display imaginary numbers on the number line, as a traditional number line is designed to be a graphical representation of the real numbers. To see the imaginary numbers represented graphically, simply input the number you would like to see. Try, for example, the input “1 + i”, http://www.wolframalpha.com/input/?i=1%20%2B%20i&t=ff3tb02i . In regards to your second questions, we are looking into this. We’ve had several requests for this. I hope that we’ve answered your questions. Thank you!

Posted by The Wolfram|Alpha Team January 16, 2011 at 11:44 pm Reply

HOW DOES ONE WRITE OUT THE INTERVAL NOTATION FOR THE ABOVE PROBLEM?

Posted by Sarah Leonard January 18, 2011 at 11:32 am Reply
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