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Sep 18, 2020 at 0:33 comment added Sidarth I don't take your time and efforts for granted. Thank you.
Sep 17, 2020 at 12:04 comment added BioPhysicist @Sidarth I answered your question a while ago before you drastically changed the question. This is poor practice because you are invalidating answers that have already been made. This site isn't a "back and forth" forum where you keep updating and changing goal posts and then expect answerers to do the same. I honestly can't even tell what you are asking anymore. Your question has become very unfocused, and I don't want to dig through comments to try to figure out what you're really after here.
Sep 17, 2020 at 11:58 comment added Sidarth @BioPhysicist I've re-read the question many times. The question remains. I still don't have a satisfactory answer. Now I am in the process of comparing infinitesimal volumes. (which actually is the original question), now, its only clearer after filling some gaps about how exactly an infinitesimal volume is formed, the concept of hyper real numbers, some knowledge about infinitesimals itself. It seems I can get a yes or no answer right? Please see my unaddressed comment to Buraian's answer as well
Sep 16, 2020 at 11:34 comment added BioPhysicist @Sidarth If your own answer is what you are looking for then you can accept it. I feel like the goal posts have been changing for this question for a while. Technically if you realized you were wanting to ask a different thing you should have asked a new question from the beginning, not update your question so that current answers became somewhat invalid.
Sep 16, 2020 at 4:52 comment added Sidarth I have added the final edit to the question which points this out. Should I ask a new question? What about the activity on this one? Frankly, comparing infinitesimal volumes has been the question all along.
Sep 16, 2020 at 3:16 comment added BioPhysicist @Sidarth Then ask a new question. Just make sure to be specific about the comparison you want.
Sep 16, 2020 at 2:09 comment added Sidarth @BioPhysicist I do know that cubes are not the only infinitesimal volumes. "... because an infinitesimal value multiplied by a finite value is still infinitesimal..." then the discussion moves to comparing infinitesimal volumes.
Sep 15, 2020 at 20:04 comment added Ryan Thorngren I'm not sure this qualifies. The basic volume element is still a prism of dimensions $r d\phi$, $r \sin \phi d\theta$, and $dr$.
Sep 13, 2020 at 16:41 history edited BioPhysicist CC BY-SA 4.0
deleted 4 characters in body
Sep 13, 2020 at 11:22 history answered BioPhysicist CC BY-SA 4.0