I hope the Computer Science section is the appropriate place to ask this question. I’m working on profiling some data sets and I am a bit tripped up on something, I was hoping I could get some assistance.

Part of my project is to determine whether some of my data is an integer and whether is a continuous or discrete quantity.

I understand that in a simple sense Discrete data is counted and Continuous data is measured. I also know Discrete Data can only take on certain values while Continuous Data can take on any values.

It seems that the size of a computer file (in bytes) could take on either of these descriptions because bytes are based on bits and are based on a power of 2 (which would make it discrete). However at the same time a file size could be Continuous because it could be of any size.

If anyone could help me out it would be greatly appreciated! Also if you are aware if I misunderstood something please let me know!

  • $\begingroup$ What exactly are you asking? $\endgroup$ – lPlant Jul 14 '14 at 19:51
  • $\begingroup$ Sorry - I'm asking whether the byte size of a file is considered Discrete or Continuous $\endgroup$ – Sami Jul 14 '14 at 20:05
  • $\begingroup$ IPlant has a good answer. In general, anything having to do with computers is discrete. The only real way to do continuous stuff is by discretization and approximation, or to use some sort of symbolic manipulation of data. $\endgroup$ – jmite Jul 14 '14 at 21:41
  • $\begingroup$ As IPlant says, the pedagogically correct answer is "discrete". However, for some statistical applications, you might be able to treat it as continuous (as a reasonable approximation). Since you haven't told us why you need to know or how you will use the information, it's hard to provide a definitive answer that will be right for your setting. $\endgroup$ – D.W. Jul 15 '14 at 0:39

A file size is measured in bits, you cannot have a portion of a bit, only a whole bit, it is a discrete quantity. Something is continuous if it can can have any possible value in a range, bounded or not. Something can be discrete and at the same time infinite.

The best way to think about discrete or continuous is if for any two values you can find a value between them then it is continuous, otherwise it is discrete.

  • $\begingroup$ Though that's not perfectly accurate. You can find another rational number between any two rational numbers, yet $|\mathbb Q| = |\mathbb N|$ and furthermore, there is no concept of continuity/differentiation in the rationals. $\endgroup$ – gardenhead Jul 14 '14 at 23:46
  • $\begingroup$ Except that, at least according to wolfram, the rational numbers are a continuous set [1] [1]: mathworld.wolfram.com/RationalNumber.html $\endgroup$ – lPlant Jul 15 '14 at 0:01
  • $\begingroup$ Hmmm I wished they linked to a definition. That's not continuous as far as I understand it (I was thinking of continuous in the calculus sense). But I have yet to take a Real Analysis course so I'm not too surprised. $\endgroup$ – gardenhead Jul 15 '14 at 1:21
  • $\begingroup$ Here is a definition from the encyclopedia of math, encyclopediaofmath.org/index.php/Continuous_set $\endgroup$ – lPlant Jul 15 '14 at 1:26

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