Definite product of zero and infinity?

[matt grime]

These do have uses in applied mathematics and are called infinitesimals, rigorously dt is a 1 form, and rearranging antonios equation yields a 1 form = a function which is not permitted, you've canceled things that can't be canelled, and your manipulations omit many equalities that need to be satisfied, you should always write out in full.

a/c is (1/c)dv/dt

I don't see how you took any of the steps above without implicitly assuming some things that you've not told us, such as somehow deciding that dv/c = 1, which is amazing as c is a constant.

 

[Antonio Lao]

Is the following limits acceptable in mathematics?

$$\lim_{dt\rightarrow 0} \frac {1}{dt} = \infty$$

$$\lim_{dt\rightarrow \infty} \frac{1}{dt} = 0$$

$$\lim_{dt\rightarrow a} \frac {1}{dt} = \frac {1}{a}$$

 

[Muzza]

The last one is invalid if a = 0...

 

[Antonio Lao]

Thanks. But if a=0, it is just the first one again. Physically speaking, can absolute time (absolute spacetime) ever be zero? Spacetime is not defined at the singularity.

 

[matt grime]

Try reading Segal's original papers to see the formalization of zero time.

 

[Antonio Lao]

Thanks. I will start looking where I can get hold of this paper.