Saturday, April 11, 2015

J is for . . .

Ready for today's Mad-Cool-Math nugget?

J is for jump discontinuity.

Here is a picture of a nice, smooth continuous function:






Image courtesy: Wikicommons

Compare that unbroken, blue swoop to this choppy, blue step function, which hops up at every number leaving a gap. Such a break is called a jump discontinuity.



Image courtesy: Wikimedia Commons

This particular step function is called a floor function. We've got two axes here: the horizontal x-axis and the vertical y-axis. Where x = 0, you see a solid blue dot. That means y = 0 there too. Where x = 0.5, y still equals 0. Where x = 0.9, y is still 0, and so on until you get to x = 1. Then the y value jumps up to 1 too.

Similarly, when x = 1.2 or 1.4 or 1.8 or 1.99999, the corresponding y is 1. Then when x = 2, y jumps from 1 up to 2.

What kind of kooky person uses something like this? You do, every time someone asks your age. 

11 comments:

  1. I never knew this had a term. Teachers don't teach that in school.

    ReplyDelete
  2. Totally lost, Think I might have seen a graph like that back in school, but lordy that was sooooooooooo long ago, back in the dark ages I don't remember a thing about it.

    ReplyDelete
  3. Step functions are quite useful for some purposes in theoretical physics, in particular the single-step function known as the Heaviside function (the function in your plot can be represented as a sum of Heaviside functions) >:)

    Cold As Heaven

    ReplyDelete
  4. This was fun! I wish I had you for a math teacher! I'm your newest follower!

    Julie

    ReplyDelete
  5. cheap nike free run shoes cheap nike free run shoes me mess with cheap nike free run shoes cheap, had his skill has reached such a state. like his face relaxed, as if he does not http://www.nikeplus.com.au bring down costs Chuihuizhili. cheap nike free run shoes bald dog but King nike free run australia himself one of the three men, how was this kid to overthrow, and this kid looks No wonder Dad will not let

    ReplyDelete

I will do everything in my power to visit commenter's blogs unless I've been abducted by aliens or my children get sick. (If my children get abducted by aliens, I will be very busy, of course, catching up on my sleep.)