Discrete or Continuous?

[sachleen]

what does discrete mena, not sure what continuous means either.

[Whiffle]

Life, time, bodily functions and many other things are all continuous in nature, as they are continuously changing. On the other hand, we humans can only comprehend continuous things when they are broken up into discrete parts. Thats how I see it anyway.

[ross206]

Are the days of the week discrete or continuous? Is your age continuous or discrete? While some may be easy to decide some are under serious thought. Many philosophical arguments are drawn from the still open idea of discrete and continuous. Discrete is a way of explaining factors that can be counted, while continuous is used to explain factors that can be measured. We can?t ever know if an example such as our weight can be labeled in a group of continuous or discrete. We do burn a continuous amount of weight, although we have a fusillade of jumps from 110 pounds to 120 pounds and back again as we eat and excrete waste. This raises the question is it possible to classify this as either one?

Please leave any ideas on the topic. Evidence to support or just another concept to present...

[ross206]

what does discrete mena, not sure what continuous means either.

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Continuous is when something changes at a constant rate like time, it changes continuously. Discrete is the exact opposite when something changes in jumps, like hours because hours change from 1 hour 2 hours and such while time can be measured to something very specific. On a graph, continuous variables would have connected dots because everything in between applies. A discrete graph has just points because you can't include anything in between them. I'll try to find examples of graphs, check back please. ;)

[ross206]

The image above is discrete because it's a graph of a sequence: 1, 4, 7, 10, 13, 16... The x-axis is showing the place in the sequence, this can only be 1, 2, 3... because you can't have a half place it's either a whole number or it doesn't apply to the sequence. In the graph we start at zero, which is the intual value but that goes into advanced algebra and brings us off topic.

Below is a continuous graph, notice how they connected the dots. This is because the volume and height are measurements. It moves up steadily not just in jumps.

[Argote]

In reality i believe days of the week and age are continuous because they can be divided into infinitely small discrete parts

[Ikkath]

Are the days of the week discrete or continuous? Is your age continuous or discrete? While some may be easy to decide some are under serious thought. Many philosophical arguments are drawn from the still open idea of discrete and continuous. Discrete is a way of explaining factors that can be counted, while continuous is used to explain factors that can be measured. We can?t ever know if an example such as our weight can be labeled in a group of continuous or discrete. We do burn a continuous amount of weight, although we have a fusillade of jumps from 110 pounds to 120 pounds and back again as we eat and excrete waste. This raises the question is it possible to classify this as either one?

There is no ambiguity whatsoever in the concepts of continuity and discrete.

We can?t ever know if an example such as our weight can be labeled in a group of continuous or discrete.

Weight or should I say mass is definitely discrete - it only appears to be continuous in everyday situations because the resolution (the accuracy) of our measuring devices are too low to observe the 'steps'.

Basically there are no continous processes in reality - they only exist in matematics (where number systems such as the real numbers have a property knowncompleteness - which basically entails that there are no holes in the numbers). Nothing as we currently understand it in reality varies continously not etime - look at this definition of Planck Time

Going back the original question:

We do burn a continuous amount of weight, although we have a fusillade of jumps from 110 pounds to 120 pounds and back again as we eat and excrete waste. This raises the question is it possible to classify this as either one?

This is obviously continuous ineveryday sense (there are no discrete jump as you imply when excretion occurs - just because the mass varies very quick does not mean it is discrete), but at a much more detailed level it can't really be continuous can it? Go back and think your definition you give above for continuity too - imagine your height measuring device can 'see' individual atoms, in this case how is the height of the water varying continously as you add more to the container... think adding oranges to a box:p. :p

[ross206]

In reality i believe days of the week and age are continuous because they can be divided into infinitely small discrete parts

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I understand the age concept because it's obviously continuous because we don't all of a sudden wake up 40 years old. The part where you say that the days of the week are continuous, aren't there only 7 days of the week, is there a 1 1/2 day in the week?

I'm not flamming but i want to press the subject and come to conscientious. :yes:

[Oompa]

Well days of the week are also a concept and are descrete because you don't say "Wednesday and half tuesday" or anything. It's just wednesday or tuesday. Age can be considered both in my oppinion. You always are aging but you don't go around saying "Oh look I am 15 and 32/100ths" or anything. But I do know people that celebreate half birthdays and stuff.

[golazo]

age-cont.

days of week-discrete

[ross206]

There is no ambiguity whatsoever in the concepts of continuity and discrete.

Weight or should I say mass is definitely discrete - it only appears to be continuous in everyday situations because the resolution (the accuracy) of our measuring devices are too low to observe the 'steps'.

Basically there are no continous processes in reality - they only exist in matematics (where number systems such as the real numbers have a property known as completeness - which basically entails that there are no holes in the numbers). Nothing as we currently understand it in reality varies continously not even time - look at this definition of Planck Time

Going back the original question:

This is obviously continuous in an everyday sense (there are no discrete jump as you imply when excretion occurs - just because the mass varies very quick does not mean it is discrete), but at a much more detailed level it can't really be continuous can it? Go back and think your definition you give above for continuity too - imagine your height measuring device can 'see' individual atoms, in this case how is the height of the water varying continously as you add more to the container... think adding oranges to a box... :p

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Dude, you have made the concept very clear, and this is a great response. I really want to congradualate u on ur intelligence and range of thought. I wish u many acollades in ur life. ;)

[Ikkath]

Well days of the week are also a concept and are descrete because you don't say "Wednesday and half tuesday" or anything. It's just wednesday or tuesday. Age can be considered both in my oppinion. You always are aging but you don't go around saying "Oh look I am 15 and 32/100ths" or anything. But I do know people that celebreate half birthdays and stuff.

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No but if you did go around saying "im 15 and 32/100th's" how would that be continuous? you are implying you only age in 100th's...

A continous quantity must be infinitely detailed - there cannot be any 'steps' in the graph no matter how far you zoom in...

Since there are physical boundaries to resolution of space, time and matter there can be NO continuous processes in the real world - even though they may seem to be continuous from our perspective (think how the world looks flat but we know its round).

Mathematically continuous has many definitions, here is one I remember off the top of my head. Some function (equation, say y=4x) is continuous if and ONLY if :

For all epsilon > 0 there exists a delta > 0 such that |y(x1) - y(x2)| < delta implies that |x1 - x2| < epsilon.

Have a good think about that (draw some graphs and see what it really means), or have a look here Continuity - bear in mind this is heavy stuff if your under 17, so dont be upset if you can't get it straight away... maybe ask your teacher if your interested...

[ross206]

486dx 66 mhz

8 mb ram

250 mb hdd

3 1/2 " floppy

windows 3.1

(haha that's hella kool,lol) :laugh:

[ross206]

No but if you did go around saying "im 15 and 32/100th's" how would that be continuous? you are implying you only age in 100th's...

A continous quantity must be infinitely detailed - there cannot be any 'steps' in the graph no matter how far you zoom in...

Since there are physical boundaries to resolution of space, time and matter there can be NO continuous processes in the real world - even though they may seem to be continuous from our perspective (think how the world looks flat but we know its round).

Mathematically continuous has many definitions, here is one I remember off the top of my head. Some function (equation, say y=4x) is continuous if and ONLY if :

For all epsilon > 0 there exists a delta > 0 such that |y(x1) - y(x2)| < delta implies that |x1 - x2| < epsilon.

Have a good think about that (draw some graphs and see what it really means), or have a look here Continuity - bear in mind this is heavy stuff if your under 17, so dont be upset if you can't get it straight away... maybe ask your teacher if your interested...

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Wow i only understood half of that but it sounds like a great suject to venture into I'll check it out (im 15 myself)

[Hum]

:huh: Ouch. This thread made me think.

Anything that can be expressed as a number, could be endlessly divided into smaller 'parts'. Time is an imaginary thing, using any unit you like.

I suppose you could divide your body down to the number of molecules, but since the body changes from moment to moment, what would be the point ?

When your get beyond the trillions, do numbers really have any useful meaning anymore ? :unsure:

[dreamz Veteran]

we need to be careful here. in particular, we need to distinguish between human-imposed discreteness (as a matter of definition) and actual discreteness (a function of the phenomenon).

discrete phenomena are those that can be counted. these are usually counted off according to the integers (naturally enough). continuous phenomena are usually modeled by real numbers.

we can note one definition of continuous functions:

f(x*) is defined and we restrict ourselves to the domain of f

lim x --> x* f(x) exists

lim x --> x* f(x) = f(x*)

we can note another, which was posted. read more here: http://mathworld.wolfram.com/ContinuousFunction.html

one interesting point is to note the relationship between continuity and differentiability. differentiability implies continuity, but there are continuous points that are not differentiable.

when we consider a normal definition, like a day, we need to distinguish between the fact that a "day" is NOT a physical phenomenon, but a human one. a day is defined to be that length of time according to some natural process (here, the earth's rotation). but that is not to say that the underlying natural function is discrete, but it means only that our definition is discrete. days are discrete because we say they are.

one anthropologist examined this notion. levi-strauss believed there were continuous processes (e.g. the light spectrum) that are anthropologically defined as discrete (e.g. colors as red, yellow, etc.).

we can also consider other notions, e.g. transfinite numbers. the continuum hypothesis inquires into the idea that there exists a transfinite number in between two transfinite numbers. as far as i know, it's undecideable.

moved here

[Ikkath]

we need to be careful here.  in particular, we need to distinguish between human-imposed discreteness (as a matter of definition) and actual discreteness (a function of the phenomenon).

discrete phenomena are those that can be counted.  these are usually counted off according to the integers (naturally enough).  continuous phenomena are usually modeled by real numbers.

we can note one definition of continuous functions:

f(x*) is defined and we restrict ourselves to the domain of f

lim x --> x* f(x) exists

lim x --> x* f(x) = f(x*)

we can note another, which was posted.  read more here: http://mathworld.wolfram.com/ContinuousFunction.html

one interesting point is to note the relationship between continuity and differentiability.  differentiability implies continuity, but there are continuous points that are not differentiable.

when we consider a normal definition, like a day, we need to distinguish between the fact that a "day" is NOT a physical phenomenon, but a human one.  a day is defined to be that length of time according to some natural process (here, the earth's rotation).  but that is not to say that the underlying natural function is discrete, but it means only that our definition is discrete.  days are discrete because we say they are.

one anthropologist examined this notion.  levi-strauss believed there were continuous processes (e.g. the light spectrum) that are anthropologically defined as discrete (e.g. colors as red, yellow, etc.).

we can also consider other notions, e.g. transfinite numbers.  the continuum hypothesis inquires into the idea that there exists a transfinite number in between two transfinite numbers.  as far as i know, it's undecideable.

moved here

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Yep - phenomenon that we label 'discrete' are usually discrete due to the nature of the definiton.

I knew there would be a nice page on mathworld - but the best I could come up with last night (tired from being up programming over 20 hours) was this hardly a nice definition to break someone in with... :p

Transfinite numbers... you gotta love Cantor and his wacky ideas! Continuum hypothesis is as you say undecidable within the 'usual' set theory framework - as it and its converse are true. So mathematically we cannot say if the distribution is discrete or continuous.

[Hitman2000]

A random variable is called discrete if it takes values

in some countable subset (fx1; x2; x3;..), only, of R. The discrete ran-

dom variable X has (probability) mass function f : R--> [0; 1] given by

f(x) = P(X = x).