The idiotic dichotomy between irrational numbers vs rational numbers is ridiculous to begin with. Irrational numbers are numbers and functions the reason why nature is filled with irrational numbers is because time and energy flow is always moving, whenever we measure something we are never measuring absolute stasis, we are measuring flow, hence the irrational numbers, if you froze time and motion you could rationalize all numbers in nature by multiplication.
How do you figure?
Think about it.
3.33 times 100 becomes 333, what you are doing is changing the scalar, to see this go get a 3D program like 3DS max or a free version of truespace, and play around with segmenting shapes into smaller and smaller pieces (adding lines of resolution/vectors, etc). An easy way to think of it is to imagine a graph in which you keep adding lines and points of resolution by making ever larger and larger numbers/functions, an easy way to think about it is to use the concepts of coloring - all filled, all empty, etc.
3.33 is not an irrational number. Multiplying any irrational number by a rational number will still result in an irrational number
You’re missing the point completely irrational number is a number AND a function, if you stopped time the "irrational number* would no longer be irrational (i.e. go on forever), because to function you need time (i.e. a vector to put the next number), I forgot to state that. Irrational numbers are functions (are the results of ratios of movement in time).
Numbers must have a location in a vector space for each unique digit (i.e. 3.14, the first 3 would be 3, 1’s, which it really is, , etc, etc).
Could you explain why an irrational number is a function or at least point somewhere for more info? I’ve never heard that before. How can it be a function of time? The value of pi is not rational, and it does not change with time, so how would stopping time suddenly make the value rational? The definition of an irrational number is a negative one, meaning that irrational numbers are defined as any real number that is not a rational number. There are an uncountable number of irrational numbers.
Ah, I see your issue. It’s a function, but not of time. Infinte series work off a generic variable, call it whatever you like, but it’s not time. Freezing time, whatever that would mean, would not change the value of an irrational number, or stop it in it’s tracks.
You guys are both right. I think my OP title was a little too grandeose. I think it should have read “there are no rational numbers in space” since it has more to do with geometry than countable objects. In other words, my argument works better with quantities that describe “how much” of something there is (like distance, angle, volume, anything spatial, etc.) as opposed to “how many” there are. And I guess you could put all these things in terms of units so that a question of “how much” volume there is can be rephrased as “how many” cubic feet there are, but I think the point here is that you might still end up with an irrational number even when measuring a certain number of units, but not necessarily. When you stick strictly to the “how much” terminology, it is necessary (not logically, but practically).
Well, by definition, measurement is an estimate. Any real scientific measurement includes not only the estimation itself (length, mass, etc), but also a margin of error, and measure of confidence.
Think of it this way, if knew the value we were looking for, we wouldn’t have to measure it, would we?
I wonder if the quantum length would come into play at some point and stop the irrationality of a measurement. But, for all intents and purposes, I’d say you are right; measurements are irrational numbers. The probability that a measurement just stops at a certain point, like 2.1231231490551340980134810329841240000000000 meters seems unlikely.
And that is where you are incorrect, we are talking about numbers made of stuff, you can’t have a number that is not made of something, when you think of a number it is made of concept-data, therefore, in order to calculate you have to be made of something, you can see this by grabbing some playdough and creating numbers out of it, once you run out of playdough you cannot create more numbers.
You’re still under the mistaken idea that math exists ‘apart’ from nature, when math is nothing more then a description of geometric structures. Again all calculation requires time, and if you represented and irrational number in binary the binary string would be growing, and each bit in the string needs a vector and location in space to be stored, if you stopped time that growth function would stop, period. So no, it has everything to do with time, if we froze time all calculation would stop.
Do you know anything about calculus? An irrational number just exists, it’s only the calculation that requires an effort on our part. Freezing time does nothing to the number. You can say that you only want to take the first ‘n’ terms of an infinite series, but that has nothing to do with time.
Here, this video should sum it up for you: youtube.com/watch?v=WrjwaqZfjIY
This was a thought that actually occured to me a few years back and I’m glad I’m not alone in the thought. My final conclusion then was that even though nothing in nature really seems to have infinite zeros after the decimal point, if we could instead measure the smallest particles (my assumption was electrons/protons/neutrons or maybe even quarks) we would have a rational number since there’s only a finite number of particles. So our measurements would be precise to the point and rational. Does this seem logical?
And to back up anthem here, math is a concept irrelevant to time so stopping time would have nothing to do with it as infinite, or finite for that matter, has no “speed(units/time)”, which seems to be your assumption superculture.
Thanks Rouz 
Yes it does, but I think the number of particles falls into the “how many” camp as opposed to the “how much” camp. When it really comes down to it, I think the “how much” camp can be reduced to only continuous quantities such as space and time (in other words, not discrete “things” that exist).
What you’ve said still doesn’t deal with my point: In the real world these numbers would go on forever, and they would have to be made of stuff, if you were to expand an infinite series, it would take up all matter in the universe pretty quickly, and you’d run out of stuff to make the next number in the series. i.e. they are numbers and functions, you have to get used to the idea that numbers are self-recursive functions, and when time stops these functions also stop
If the ratio 1/3 is a function, then it’s opposite 3/1 is a function and since even “irrational” numbers have a base, that means they must by definition be numbers and functions, for math to remain consistent, remember all numbers are made of the first, that is, 1. Therefore:
Pi is actually Pi / 1 (which is a function), you can only see it by representing numbers in total expanded form using shapes, and ‘stuff’ to make numbers out of. Numbers are not made out of non-existence, they are made of stuff that exists.
What you’ve said is pure bullshit, numbers are functions, and functions only function if there is time, numbers are not made of non-existent stuff, I want you to grab apiece of paper and cut it into equal pieces and for each element of a number (say, 2 there is 2 squares, 3 there is 3 squares and so on), soon enough you’ll run out of stuff to make numbers out of, your fallacy is that you think numbers are made out of non-existent stuff, that is why you can’t grasp what I am saying and it is not an assumption it is a fact, you can’t get a non-existent number from non-existence, period.
There needs to be a distinction between counting and measuring. You can count the number of atoms along the length of a piece of wood, and get a rational number, but how long is each atom? You end up with the same problem. And as we deconstruct particles further we find that the smallest parts may not even really exist at all times ( 
quantum physics is crazy). It’s murky ground still, but the point is we can’t get exact measurements because we still don’t understand what goes on at the smallest levels
Ok, are you saying that you need to time to count digits, so that if time were stopped there would be no time to count digits and therefore the digit after you no longer can count no longer exist? That makes no sense to me. And why insist that numbers are made of physical stuff? Counting, and assigning numbers to things is a human concept. The fact that we use base 10 to count, or bases 2 and 16 in computers is an arbitrary human decision. Numbers, counting, units of measurement - all are human concepts that we use to describe what we see. Numbers don’t have to exist in nature, only in our heads, and if that’s the case, then there is no reason to limit them
Always good to see the products of an engineer’s mind 
Are you still a student by the way or postgrad, what are you studying?
Yup yup but a great many of these particles are naturally restricted to bigger particles and the smallest particles only exist at very small fractions of time and not in all conditions so it would be possible to get matter to a point where these particles won’t be emitted randomly, as far as I’m aware. Measuring them in a hypothetical scenario still makes sense, we just don’t have any equipment to measure something to that smallest possible point. I’m assuming there is a smallest fraction. Perhaps something like an Avogadro’s number for length? My assumption is that since everything is finite from base to whole, if we were to make an infinitely accurate measuring device, we’d end up with a rational number.
I used to think of the possibility of “smallest possible movement” by any particle which would imply that a particle can only move 0.00…1m at a given time and not 0.00…05m to rationalize movement as finite as opposed to infinitely small. Possible?
If self-righteousness and emotionally triggered insults were indicators of being correct, you’d be have the final say. Numbers are concepts. You’ve said “if you were to expand an infinite series, it would take up all matter in the universe pretty quickly”. We’re saying it doesn’t do it “pretty quickly”, it doesn’t have time. Two infinites don’t reach a given number at different times, infinite doesn’t work with speed, it isn’t a number, it’s a concept and it’s irrelevant to time. Freezing time doesn’t let you count [x/0] or pi, assuming you weren’t frozen. Pi will be irrational at 0 time or at infinite time.
You’re assuming that things are constantly growing in time as one goes to smaller measurements. I assure you they aren’t. You can measure the weight of something (and weight measurements are quite accurate), and then measure its length to the smallest possible accuracy. Its weight won’t change regardless of how small you go. Freezing time is irrelevant.
Saying something is bullshit just shows that it opposes your views and that you’re disrespecting the person due to an inability to present a viable argument. If you can’t discuss a logical problem without emotions then there’s nothing to discuss, only argue, which I have no interest in.
youtube.com/watch?v=WrjwaqZfjIY
You have no idea what a function is. I’ll give you the 7th grade definition:
Numbers are numbers. 3/1 is not a function, it is a number. 3/1 = 3 is an equation. 3/x = y is a function. The solution to the algebraic equation 3/x = 1 is 3.
A function doesn’t need time to work, it just needs an input. The input could be time, or it could be distance, or pressure, or just another number.
Now, what you’re saying about freezing time and thus ending existence is another subject. If we don’t exist, then we can’t do math, fair enough. Probably numbers wouldn’t exist, either. However, if you were to just freeze time within existence, irrational numbers would still be infinitely long. Math is a self-contained language within existence, whether made by man, made by nature, or as man’s convenient way of representing a language made by nature.
Final semseter of mechanical undergrad coming up. I saw your profile, are you still a student?