A discrete mass distribution is made up of point masses arranged in fixed relative positions. To find the mass, centre of mass or moment of inertia you use summation. The density of such a body is non-uniform, it varies from place to place : it is infinite at the point masses and zero elsewhere.
Discrete mass distributions are hypothetical. They don't exist in the real world because point masses don't exist. All mass occupies a finite amount of volume. However, if the mass of an object is concentrated in regions which are small compared with the size of the object, then those regions could be treated as point masses.
Examples : a dumbbell/barbell is usually treated as two point masses at the ends of a massless rod; a simple pendulum is a point mass at one end of a massless string or rod.
A continuous mass distribution is spread out in space. Every point within the body is connected to the whole, there are no gaps. If the density is the same at all points within its boundaries it is uniform. To find the mass, centre of mass or moment of inertia of a continuous body you might have to use an integral, ie a summation of an infinite number of infinitesimally small parts in which the density is uniform. Integration is usually necessary if the density varies from one place in the body to another.
Examples : a solid sphere or cube, which usually have uniform density if made out of a single material such as wood or iron. The Earth and other planets have non-uniform density; they are more compressed towards the centre because of gravity.
An object can be a mixture of continuous and discrete mass distributions.
Answer from sammy gerbil on Stack ExchangeQuora
quora.com › What-are-some-examples-of-objects-that-have-continuous-motion
What are some examples of objects that have continuous motion? - Quora
Answer (1 of 2): 1. Light 2. Planets 3. Asteroids 4. Comets 5. Stars 6. Atoms (vibrating) 7. Electrons ( while in atom vibrating and while flowing moving from one atom to another) 8. Electromagnetic radiation The names that I have given never stops in their life time. I mean light moves for ever ...
ArcGIS
desktop.arcgis.com › en › arcmap › latest › extensions › 3d-analyst › discrete-and-continuous-data-in-3d-analyst.htm
Discrete and continuous data—ArcMap | Documentation
Surfaces are continuous data, such as elevation, rainfall, pollution concentration, and water tables. This data can be represented as a continuous surface, generally without sharp or abrupt changes. ... Discrete features are discontinuous and have definite feature boundaries.
Does continuous exist in real life?
Does continuous exist in real life? Our most accurate models of physics have full continuity as a feature — even in quantum mechanics, where the fields take on discrete values, spacetime itself is still modelled as a continuum (or rather a manifold, which is a continuous mathematical structure with an uncountably infinite number of points and which is infinitely subdivisible), and there are various continuous symmetries present which play important roles, such as in conservation laws via Noether's theorem . Much of modern physics is written in the language of calculus/analysis and differential equations; even Schrödinger's equation, the wave equation arguably at the heart of quantum mechanics, is a differential equation. Let's consider this experiment: ... -> The car must move through all of these infinite speeds in 9 seconds. So: -> From a physics perspective we have "something", that moves infinite time in 9 seconds, so this "something" has infinite velocity (and is greater than C), and there is no physical thing that has bigger velocity than C. Can you help me understand what I'm missing here? And each of those infinite speeds takes an infinitesimal amount of time. Or more accurately, a differential amount of time — you know, in the calculus sense: dx/dt. What you seem to be trying to describe is an analogue of Zeno's paradox ; this apparent paradox was resolved with the advent of calculus. The tools of calculus provide the means to derive finite answers from calculations involving infinitesimal/differential change and/or infinite sums. For example, there is a formal way to show that the sequence 1/2 + 1/4 + 1/8 + 1/16 ... converges to a value of exactly 1. The value of the sum is not infinite just because there are an infinite number of ever-increasing terms — the sum converges on a finite limit. The velocity of the car you describe is never infinite; it is always finite. At any given moment the car will have a finite velocity; assuming constant acceleration, it will only ever have a given velocity at a precise instant in time. By carefully taking limits, derivatives, etc. you can determine what that velocity will be at any given time, but neither the velocity nor the elapsed duration (9 seconds) are ever infinite. (I believe that there is nothing continuous in life, everything is discrete.) Well, I'm afraid your belief here is unfortunately misguided ... as it is in conflict with modern physics. Best to reconcile this belief and update it as you learn more! Hope that helps, More on reddit.com
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March 5, 2024What are good examples of discrete and continuous data?
The examples of (the number of) sweets and books are fine. You just have to assume (for the sake of counting) that these are indivisible units, as they are in reasonable situations. Perhaps more clearly indivisible is a banknote or a coin. You can break it in two, but it doesn't give you two objects with half the value. More on reddit.com
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January 10, 2016Videos
OpenGeoEdu
learn.opengeoedu.de › en › gis › vorlesung › geodatenmodellierung › diskret_vs_kontinuierlich
Discrete versus continuous objects | OpenGeoEdu
The choice of describing an object as a discrete or continuous phenomenon not only influences the geometric modeling; it also implicitly determines topological relationships and the assignment of thematic and temporal properties to the object. It is possible to switch between discrete and continuous representations, depending on the question, the degree of detail, the method of recording and the ability to concretize. A good example of this is the description of a terrain surface in the form of a Digital Terrain Model (DTM), which can be represented on the one hand by regular grid cells in raster data form, but on the other hand also by triangles as vector data in the form of a triangular mesh.
Esri
webhelp.esri.com › arcgisdesktop › 9.2 › index.cfm
ArcGIS Desktop Help 9.2 - Discrete and continuous data
September 22, 2008 - We cannot provide a description for this page right now
material
toposuranos.com › portada › the latest › continuous bodies in physics: from point-like to continuous
Continuous Bodies in Physics: From Point-like to Continuous - toposuranos.com/material
December 30, 2024 - Although nature does not present point-like objects, this approach makes sense because it allows us to address concepts more simply and understandably. Newtonian mechanics, for instance, was developed before the physics of the continuum, so it is important to have some familiarity with its laws to understand how continuous objects, which are composed of a large number of tiny particles, can “simulate” the continuity we observe in nature.
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In combinatorics, there is no shortage of functions that are hard to compute. Here are two famous examples whose input is a simple graph 
: · 
size of the largest independent set 
· 
size of the largest cut-set 
· Both of these discrete functions are 
-hard to compute. However, there are polynomial time–computable functions 
and 
that map simple graphs to real numbers (i.e., continuous quantities) in a way that monotonically decreases and converges pointwise to the desired functions. · Warning: While the runtime of the 
th function is polynomial for a fixed precision (at least under certain models), the exponent increases with . See this thread for more details on runtime considerations for semidefinite programs. · To be explicit, 
denotes Schrijver's strengthening of Lovász's semidefinite relaxation of the independence number, 
denotes the Goemans–Williamson semidefinite relaxation of maximum cut, and the sequences arise from sum-of-squares hierarchies that strengthen these relaxations. The claimed pointwise convergence is a consequence of the identities · 
· which follow from results in [Lasserre 2002] and [Fawzi-Saunderson-Parrilo 2016], respectively.
: · size of the largest independent set · size of the largest cut-set · Both of these discrete functions are -hard to compute. However, there are polynomial time–computable functions and that map simple graphs to real numbers (i.e., continuous quantities) in a way that monotonically decreases and converges pointwise to the desired functions. · Warning: While the runtime of the th function is polynomial for a fixed precision (at least under certain models), the exponent increases with . See this thread for more details on runtime considerations for semidefinite programs. · To be explicit, denotes Schrijver's strengthening of Lovász's semidefinite relaxation of the independence number, denotes the Goemans–Williamson semidefinite relaxation of maximum cut, and the sequences arise from sum-of-squares hierarchies that strengthen these relaxations. The claimed pointwise convergence is a consequence of the identities · · which follow from results in [Lasserre 2002] and [Fawzi-Saunderson-Parrilo 2016], respectively. 2 of 6
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Mirco, regarding your second question (emergence from the continuum): My view would be that the FUNDAMENTAL GROUP of topological objects is an example. It captures discrete properties of a continuous object, e.g. a sphere. Or seen as the deck transformation group, it expresses the discrete structure of the universal cover of a continuous object like torus, sphere, and so on.
Wikipedia
en.wikipedia.org › wiki › Continuous_function
Continuous function - Wikipedia
5 hours ago - A stronger form of continuity is uniform continuity. In order theory, especially in domain theory, a related concept of continuity is Scott continuity. As a practical example, the function H(t) denoting the height of a growing flower at time t would be considered continuous.
Wikipedia
en.wikipedia.org › wiki › Discrete_mathematics
Discrete mathematics - Wikipedia
March 31, 2026 - The truth values of logical formulas usually form a finite set, generally restricted to two values: true and false, but logic can also be continuous-valued, e.g., fuzzy logic. Concepts such as infinite proof trees or infinite derivation trees have also been studied, e.g. infinitary logic. Set theory is the branch of mathematics that studies sets, which are collections of objects, such as {blue, white, red} or the (infinite) set of all prime numbers.
Mathematics LibreTexts
math.libretexts.org › campus bookshelves › monroe community college › mth 210 calculus i (professor dean) › chapter 2 limits
2.6: Continuity - Mathematics LibreTexts
December 21, 2020 - Consequently, we know that \(f(x)=cosx\) is continuous at 0. In Example we see how to combine this result with the composite function theorem.
Reddit
reddit.com › r/askphysics › does continuous exist in real life?
r/AskPhysics on Reddit: Does continuous exist in real life?
March 5, 2024 -
Let's consider this experiment: a simple car accelerating from 0 to 100 km/h in 9 seconds.
->From a mathematical perspective, the car's speed must pass through each velocity between 0 and 100. So:
-> The car must be at each of the infinite number of speeds between 0 and 100. So:
-> The car must move through all of these infinite speeds in 9 seconds. So:
-> From a physics perspective we have "something", that moves infinite time in 9 seconds, so this "something" has infinite velocity (and is greater than C), and there is no physical thing that has bigger velocity than C.
Can you help me understand what I'm missing here?
(I believe that there is nothing continuous in life, everything is discrete.)
Top answer 1 of 5
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Does continuous exist in real life? Our most accurate models of physics have full continuity as a feature — even in quantum mechanics, where the fields take on discrete values, spacetime itself is still modelled as a continuum (or rather a manifold, which is a continuous mathematical structure with an uncountably infinite number of points and which is infinitely subdivisible), and there are various continuous symmetries present which play important roles, such as in conservation laws via Noether's theorem . Much of modern physics is written in the language of calculus/analysis and differential equations; even Schrödinger's equation, the wave equation arguably at the heart of quantum mechanics, is a differential equation. Let's consider this experiment: ... -> The car must move through all of these infinite speeds in 9 seconds. So: -> From a physics perspective we have "something", that moves infinite time in 9 seconds, so this "something" has infinite velocity (and is greater than C), and there is no physical thing that has bigger velocity than C. Can you help me understand what I'm missing here? And each of those infinite speeds takes an infinitesimal amount of time. Or more accurately, a differential amount of time — you know, in the calculus sense: dx/dt. What you seem to be trying to describe is an analogue of Zeno's paradox ; this apparent paradox was resolved with the advent of calculus. The tools of calculus provide the means to derive finite answers from calculations involving infinitesimal/differential change and/or infinite sums. For example, there is a formal way to show that the sequence 1/2 + 1/4 + 1/8 + 1/16 ... converges to a value of exactly 1. The value of the sum is not infinite just because there are an infinite number of ever-increasing terms — the sum converges on a finite limit. The velocity of the car you describe is never infinite; it is always finite. At any given moment the car will have a finite velocity; assuming constant acceleration, it will only ever have a given velocity at a precise instant in time. By carefully taking limits, derivatives, etc. you can determine what that velocity will be at any given time, but neither the velocity nor the elapsed duration (9 seconds) are ever infinite. (I believe that there is nothing continuous in life, everything is discrete.) Well, I'm afraid your belief here is unfortunately misguided ... as it is in conflict with modern physics. Best to reconcile this belief and update it as you learn more! Hope that helps,
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-> From a physics perspective we have "something", that moves infinite time in 9 seconds, so this "something" has infinite velocity (and is greater than C), and there is no physical thing that has bigger velocity than C. First of all, speed is distance over time, not time over time; your phrase "infinite time in 9 seconds" makes zero sense. Comparing it to other speeds thus makes equally little sense (zero). Secondly, the set of real numbers is uncountable, so talking about moving through "infinite speeds in 9 seconds" is meaningless, because you can equally well say that the time spent at each speed is infinitesimally small. No matter how much you divide it into different speeds, there exists a possible time spent at each speed to make the total time become 9 seconds. This is all very basic calculus, which you should consider picking up a textbook on if you want to learn the relatively simple mathematics behind it.
Reddit
reddit.com › r/math › what are good examples of discrete and continuous data?
r/math on Reddit: What are good examples of discrete and continuous data?
January 10, 2016 -
I recently watched a lesson about this and so many kids were confused. The teacher said sweets were discrete and also books. However, the students said you could have all sorts of sweet sizes if a sweet broke so wouldn't it be continuous. The same with ripped books that were still being used but the book is in two halves or 1/4 and 3/4 etc.
Even shoe size was quetioned as of places that customize shoes for you so you get a more accurate size and not the usual discrete shoe sizes that we are used to.
What I'm looking for is good examples for discrete data. I thought discrete could be living humans as I can only think of students saying you can be half dead which I could explain how that isn't really measurable.
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The examples of (the number of) sweets and books are fine. You just have to assume (for the sake of counting) that these are indivisible units, as they are in reasonable situations. Perhaps more clearly indivisible is a banknote or a coin. You can break it in two, but it doesn't give you two objects with half the value.
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I think the most common example I've seen of discrete data points is in probability, when you're considering the outcome of the roll of a die. You can roll any of {1, 2, ... , 6}, but these are your only possible outcomes. You cannot roll 2.5 or 3.7 or any number that isn't an integer from 1-6.
Geospatial
vector.geospatial.science › textbook › chapter-three › discrete-and-continuous-data
Section Four - Discrete and Continuous Data | Vector Based GIS
A discrete object has known and definable boundaries: it is easy to define precisely where the object begins and where it ends. . For example, a Digital Elevation Model ( DEM Digital Elevation Model ) represents continuous elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl.
Physics LibreTexts
phys.libretexts.org › campus bookshelves › georgia state university › gsu-tm-physics i (2211) › 6: mass, and inertia
6.5: Center of Mass of Continuous Objects - Physics LibreTexts
February 24, 2025 - We will keep this simple by restricting ourselves to objects for which the position of the center of mass in two of the three dimensions is obvious. A good model for this is a simple thin, cylindrical rod. This rod's mass distribution is completely cylindrically symmetric, which means that the center of mass lies on the axis passing through its center. But the mass distribution as a function of position on this axis may not be uniform. For example...
Cuemath
cuemath.com › calculus › continuous-function
Continuous Function - Definition, Examples | Continuity
Answer: The function f(x) = 3x - 7 is continuous at x = 7. Example 2: Prove that the following function is NOT continuous at x = 2 and verify the same using its graph. Also, mention the type of discontinuity.
Mathwords
mathwords.com › c › continuous.htm
Continuous — Definition, Meaning & Examples
Real Numbers — The standard example of a continuous set · Set — A collection of distinct objects or numbers
Colin McGinn
colinmcginn.net › home › uncategorized › discrete and continuous
Discrete and Continuous - Colin McGinn
December 7, 2019 - Not objects or things–for then ... time are the paradigms, but we also regard other things as continuous: intensity of emotion, milk and honey, geometrical figures, colors, motion, fundamental matter....
ALLEN
allen.in › home › jee maths › continuity
Continuity of Functions: Definition, Properties, Solved Examples
July 9, 2025 - In summary, the greatest integer function is continuous between integers but discontinuous at integer values. Its discontinuities occur as step functions, resulting in a piecewise continuous function. ... Example 1: Determine whether the function f(x)=x−2x2−4 is continuous at x = 2.
Mit
computationalthinking.mit.edu › Fall22 › data_science › discrete_and_continuous
Discrete and Continuous — Interactive Computational Thinking — MIT
Section 2.7 · Discrete and Continuous · Lecture Video
Geography Realm
geographyrealm.com › home › articles › what is continuous versus discrete data in gis?
What is Continuous Versus Discrete Data in GIS? - Geography Realm
August 13, 2024 - This continuous raster data set ... Landsat-8, and the ESA Copernicus Digital Elevation Model (DEM). Elevation, slope, temperature, and precipitation are examples of datasets that are continuous....