CuriosOne

Still sort of confusing becuase all I see are 6 sides of 1 dimension ( 1 flat hyper plane of 6) and rotations look reflected on all 6 dimensions of the box. Its mind boggling...Atleast its how I perceive it to be.

Very insightful thXxxx... The definition of zero being a number now answers most of the point of calculus, "But" in regards to arbitrary small differences not being numbers, what are they?? functions?? I read?? My focus then would be on the operators on simple functions that output other functions not numbers as converged "things" whatever they connect to at this point. From what I'm understanding it sounds like a terrasac hypercube with infinite limits of functions within functions of operators...Is this right? If "things" are converged I can see why this would be the case in regards to a refference atlas like cartessian space and the "points" on it in 3d, hieght, width and depth.. Is this the way to think about it? The Greek lower case delta δ has my attention now. This Makes Sense ThnXxxx The second one is important to us because it is not only about small differences in the values of the variable that follows it, it is about arbitrarily small differences. This means that δx is not exact but may be made smaller and smaller indefinitely. So it is not a number it is a sort of function. Also since it is not a number it can never be zero, since zero is a number. This brings us neatly to the idea of limits.

This is getting very intresting now... I'm glad I posted this OP bold question, this information is inspiring thnXxxxx.

Will definetly try this out, looks fun thnXxxxx...I will try too slow down too, I agree with you...

If getting closer "Where is x at then?" At the edge of space??? And how do we know how far to zoom in and out, x is not a camera lense..😎

KE = (1/2) mv^2 looks correct...

"I do get what your saying" But its said Newton used the pyramids to create calculus...Is this true?? The extent of pi and the pythagorean theorem used in calculus "right angle" triangles leads one to think the pyramid contribution may be true... Even E=mc^2 looks very familiar to F=mv^2.... This explanation is very helpfull, thnXxx and your right about x=0 If x=5 but you can't reach zero, is there a sequence of numbers going on, such as a list for x and y values?? I assume that's what they are..Maybe you can show that list, as I just place it in my calculator and press generate list this is what I got...

Understood, and thnXxx. Now if u may please, for the time dimension (t) is this the fourh dimension? If so does it work the same as with the 3rd dimension ie x y z translations? Do we even use the fourth dimension for any purpose other than time?

Which dimension goes up and down? Say as we perceive falling objects from a building down to the ground with the force of gravity of coarse acting on it bouncing up then repeating till it stops.

Sounds very intresting...."in regards to tossing a dart on a board bull's eye with both in circular motion"... Where could I see a formula for this if you may?

Understood, but earth and the asteroid are in motion right? There is a reason I ask. Sounds like this only works for close range proximity? I assume.. Sounds like calculus..😎

This is more clearer and thanks.. I'm trying to tie this concept in with the pythagorean theorem since it does use some concept of geometry.. Much like music in mono and stereo, there is a big difference, but it still is what it is....Hymmm maybe being an advance human has its advantages who knows..

3rd dimension equivalent to height ,depth and thickness, what about 'scaling' making something bigger or smaller? Can I see an example of the rocket reaching an asteroid, and the time example to hit the asteroid please..

So the 3rd dimension is an illusion?

What is the 3rd dimension and how do we visualize it?

Why do we need to imagine it as I thought our concept of geometry was 3 dimensional.. And I need to add this question: Is Time One Dimensional?

Thnks for the link...I do hope however I can have some answers to my question about limits earlier....in regards to: Lim x->0 = x^2 -25/ x-5 BEFORE" we add numbers let's speak reason "please." does x^2 -25 represent y the numerical value, the value that does not change? and does x-5 represent the changing variable x? Where do these changes in position take place??? Do they take place on the orbital paths themselves, since "force" causes the planets to move?? Looks like orbital paths are "discountious" to me, hence the Title of my post. So Calculus is a tool for orbits and nothing else??

I've read number theory could be the more suitable approach as to use the number theory finds and apply them or plug them into our f(x) function limit issues. After all, there has to be many variations that define the same value as there is many ways to play the drums to a melody....I guess it depends on reliability, trust and efficiency at this point if the world depended on such a system. Yes, differential calculus focuses on rates of changes and the ""Pythagorean Therom"" is extensively used with it. The notation that expresses these functions also change which gets very frustrating, here is an example: dy/dx or df/dx or df(x)/dx or D, xy or d/dx or f'(x) or y' and etc etc "All Mean The Same Thing." Ive been observing this for years now of which had me confused for about 4 years until I caught onto it.. let me show a number example of these limits finally "I found one" and we can dissect this from here as a visual guide for direction, becuase the functions are confusing me and maybe others.. Lim x->0 = x^2 -25/ x-5 as "delta" x approaches 0 "BEFORE" we add numbers let's speak reason "please." does x^2 -25 represent y the numerical value, the value that does not change? does x-5 represent the value that does change?

Let's say the interest is 2 stationary vibrating "particles" in space (a,b )and we want to know how the "vibrations" of both interact within a certain "limit "before" change...Or even better, we want to know "which vibration is a or b, since they are all mixed in with each other...If that's even possible if this were a case involving trillions of stationary particles vibrating in space..

I have "no" relation to Idon'tknow. I read your reply, thanks "very helpfull." As per limits ""a value of plus and minus "infinity" ?? "" Is "dy/dx" infitismally small values of infinity?? What are those values of infinity then then? And why say these are limits x->0 when they are considered infinite?

I was told there is a big difference between variables and numbers... Variables change, numbers are just numbers. A limit has a value, and x can never = 0 So 0 "does" have a numerical value? It must if it plans to reach a known numerical limit of observation. ""Who decides this?"" Make note, we are following a curve here.. My entire perspective has changed, now....

Definetly would love to continue going down the rabbit hole...At this point and step by step I think first we should define what time is and I think its important here. Is time 1 dimensional? In simple words: Why do we use the speed of light as a reference for time? Yes, in regards to limits..

Understood, but one thing to consider is that all these situations follow a curve path, the points referencing "changes" need to lie on the path or curve itself otherwise calculus would render itself useless..I should have asked what's the point of cartessian space.... The distance example I assume holds only true for "linear motion" but really I was never sure of that after learning linear algebra and signal processing. The point here is that in an f(x) function the linear coorididents of x and y connect to the curve points of x and dx on the "curve" path "in cartessian linear coordinates" that does not make sense. But VIOLA! Maybe That's Why Calculus Was Invented And Maybe My Thinking Is Correct! ButI still, if x can never be = 0 does all this explain my confusion? Note: I think x can never be =1 in my opinion.

I didn't say I don't understand it, I just don't understand "tradition." Its tradition to use calculus "centuries old" math tool "contribution of Newton I assume" to derive spontaneous changes of something x "accelerating" from rest mass." Again x=0, really what's the point? "That's just one example" of the many when dealing with masses and gravity "freely flying objects" due to some force or force of attraction, be it electrical forces or gravitational forces that create motion." And yet gravity is a macro external force? I assume Newton knew before we all did, whom knows.. "In my opinion and observation of calculus itself" The whole things works just fine, until light photons start acting "strange" as particles and waves with their own unique frequencies of "pie." Note: ""The wave function used in quantum mechanics for example uses pi extensively, in fact they make focus the use of sin and cos respectfully."" Is that why x = 0? does this mean massless something?? It makes sense to believe so, unless someone can explain x=0 when dealing with accelleration and rates of changes or x= anything 0 at all at this point.. From what I see if their is no gravitational force or any force involved our x stays put and does nothing at all?? These are "ideas" like the ideas of Eistein, Plank and the others, they seem to work and have withstood the test of time, but does not explain the most simple questions.

"Maybe" I should have said: f(x) As delta x->0 towards the slope of the secant line relative to the tangent line.. But x never actually gets close to zero..I learned this 10 years ago...Does that make better sense? Book Reference: Calculus The Easy Way, Chapter 1 page 8. Sure there are places where x=0 within a curve, but I will save that for a later thread. So we should assume centuries later its handy for us??