Do divergent series converge in reality ?

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Convergence and divergence are abstract mathematical concepts and there is no physical reality to them.

In the real world one cannot add an infinite number of terms together.

So in the real world there are only finite series, not infinite series.

ruveyn

^^^^^^ This

Anytime someone uses "infinite" and "reality" together I cringe as while much of mathematics relies on the concept of infinity in reality such a thing is not possible.

Divergence requires infinity to function as a concept but in reality any series would require time to exist and therefore infinite time to be a truly divergent series and that's where it breaks down. Either at some point it ceases to exist or it can only be theorized to be infinitely existing.

There is a physical limit to how fast a circuit can active. One runs into the speed of light and the Heisenberg Uncertainty Principle.

When the time interval approaches zero energy become indeterminate.

ruveyn

I did it just now.

I went all the way to the end: adding one plus one. plus one....

And they never converge.

Did it in my head.

Okay- I admit it- I did use my check balancing ap in my computer to help.

But yeah- I got to the end of the numbers - and they never converge.

It got scary for a moment. And it looked they were about ot converge around the Googol (ten to the hundreth power). But then the numbers veered back to the same road again, and kept right on going.

So -yeah- they never converge!

While in the case of 1-1+1... the series does not converge to 1/2, or anything for that matter, the value of 1/2 "makes sense" in that it's the expected value of the sum, if one were to stop summing at an arbitrary, random place. This is true for any sum that alternates between increasing and decreasing, but where the "midpoint" between the minima and maxima doesn't "drift" (like it does for, as an example, 1-2+3-4).

However, it makes no sense at all to me to assign a sum to a series that uniformly increases, and by an increasing amount with each term. Even if you can fit a continuous function to the discrete "jumps", that function is certain to approach infinity, so there's no help there.

As someone said, if there is a series or formula in physics that diverges, it means the physics is incomplete. For instance, the existence of quantum mechanics was inferred by Planck on the basis that a collection of oscillating charged particles in thermal equilibrium would, by classical mechanics, emit an infinite amount of electromagnetic energy.