Body: <p>A function <span class="math-container">$f$</span> is said to be continuous at a point <span class="math-container">$c$</span> if it satisfies three properties:</p>
  <ol>
  <li>Should be defined at the point <span class="math-container">$c$</span></li>
  <li>Left and right-hand limits at <span class="math-container">$c$</span> must be equal i.e., the limit must exist</li>
  <li>Limit value at point <span class="math-container">$c$</span> is equal to the actual value of the function at c</li>
  </ol>
  <p><em>In short</em>:   <span class="math-container">$\lim \limits_{x \rightarrow c} f(x) = f(c)$</span></p>
  <p>I want to know whether the functions that we want to learn through real-world data, say generator in GAN, such as images, audio, video, text corpora, etc., are continuous or highly discontinuous in general? If discontinuous, what might be the reason for discontinuity? I mean, which among the three properties mentioned got a violation in the majority of cases?</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-08-22T01:41:28.737Z
Comments.Text: As said in the description, discontinuity is a property of the function. So, we can't talk of it just by looking at the data. It all depends on what kind of function to define over it.
Comments.UserDisplayName: SpiderRico
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-08-22T01:45:05.690Z
Comments.Text: @SpiderRico I mean suppose I want to learn a generator, Then the function is the function of generator neural network...
Comments.UserDisplayName: hanugm
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-08-22T01:46:35.013Z
Comments.Text: @SpiderRico so are you saying to narrow down the function I want to simulate?
Comments.UserDisplayName: hanugm
Tags: <datasets><math><data-preprocessing><function-approximation>
Title: Is it true that real world data is highly discontinuous?
UserDisplayName: hanugm
ThreadText: # Is it true that real world data is highly discontinuous?
  
  (Asked by: username_0 on 2021-08-21)
  
  A function $f$ is said to be continuous at a point $c$ if it satisfies three properties:
  
  1. Should be defined at the point $c$
  2. Left and right-hand limits at $c$ must be equal i.e., the limit must exist
  3. Limit value at point $c$ is equal to the actual value of the function at c
  
  *In short*: $\lim \limits\_{x \rightarrow c} f(x) = f(c)$
  
  I want to know whether the functions that we want to learn through real-world data, say generator in GAN, such as images, audio, video, text corpora, etc., are continuous or highly discontinuous in general? If discontinuous, what might be the reason for discontinuity? I mean, which among the three properties mentioned got a violation in the majority of cases?
  
  **Tags:** datasets, math, data-preprocessing, function-approximation
  
  > **Comments:**
  > **username_1**: As said in the description, discontinuity is a property of the function. So, we can't talk of it just by looking at the data. It all depends on what kind of function to define over it.  
  > **username_0**: @username_1 I mean suppose I want to learn a generator, Then the function is the function of generator neural network...  
  > **username_0**: @username_1 so are you saying to narrow down the function I want to simulate?  
  
  ---
  
  ## 0 answers
  
  