<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>

CC BY-SA 4.0
2021-08-22T01:41:28.737Z
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.
SpiderRico
CC BY-SA 4.0
2021-08-22T01:45:05.690Z
@SpiderRico I mean suppose I want to learn a generator, Then the function is the function of generator neural network...
hanugm
CC BY-SA 4.0
2021-08-22T01:46:35.013Z
@SpiderRico so are you saying to narrow down the function I want to simulate?
hanugm
<datasets><math><data-preprocessing><function-approximation>
Is it true that real world data is highly discontinuous?
hanugm
# 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?  

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## 0 answers

