- #1
sludger13
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I always thought the derivatives (or generally any operation with infinitesimal (infinitely large) values) belongs to the different infinity (= it is different variable). And obviously, there is no transition between two infinities (that is why is it different variable - e.g. big bang singularity problem).
I thought every time only one infinity can be intended as real, in that case other infinities are just inf. smaller (i.e. [itex]0[/itex] is expressing all values of smaller infinity) respectively inf. larger (i.e. every real value can be expressed only as [itex]0[/itex] in larger infinity). But with this approach I stumbled.
As I think about it, I realized that something (let's call it a reality) is always overstated to all infinities, making every single infinity REAL (simultaneously, no matter those are different infinities). Thus I can write real values ([itex]5,26,356,-14...[/itex]) of different derivatives (i.e. different infinities) side by side, although they are infinitely larger each other. Or I can solve differential equations.
This illustrates the image:
https://www.physicsforums.com/attachment.php?attachmentid=70445&stc=1&d=1402254253
So I want to ask: is it true consideration? Because I doubt it a little bit. For example in the picture: [itex]dx_{1}[/itex] should be infinitely smaller than the rest of real graph, as I previously thought. Real ratio of those two variables evokes for me that they belongs to the same infinity.
I thought every time only one infinity can be intended as real, in that case other infinities are just inf. smaller (i.e. [itex]0[/itex] is expressing all values of smaller infinity) respectively inf. larger (i.e. every real value can be expressed only as [itex]0[/itex] in larger infinity). But with this approach I stumbled.
As I think about it, I realized that something (let's call it a reality) is always overstated to all infinities, making every single infinity REAL (simultaneously, no matter those are different infinities). Thus I can write real values ([itex]5,26,356,-14...[/itex]) of different derivatives (i.e. different infinities) side by side, although they are infinitely larger each other. Or I can solve differential equations.
This illustrates the image:
https://www.physicsforums.com/attachment.php?attachmentid=70445&stc=1&d=1402254253
So I want to ask: is it true consideration? Because I doubt it a little bit. For example in the picture: [itex]dx_{1}[/itex] should be infinitely smaller than the rest of real graph, as I previously thought. Real ratio of those two variables evokes for me that they belongs to the same infinity.
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