degening

degening t1_jeb177b wrote

Like all paradoxes it is only a problem because when proposed there was a lack of mathematics knowledge. Lets look at the paradox in a different way:

How long does it take Achilles to reach the tortoise?

One way to solve this is to just add up all the time intervals for each step. So it takes Achiiles some time, t^1 to get to point A, t^2 to get to point B and so on. Our total time, T, is then:

T= t^1 + t^2 + t^3 .... for an infinite number of intervals.

So how do we get a finite number from adding an infinite number of positive values together? Without calculus we can't solve this and hence the paradox.

0

degening t1_jdst1be wrote

Mostly a numbers game but some pretty bad decisions were also made especially later in the war. The US was the largest industrial power by a wide margin and practically immune to attack on the mainland. Germany could never match the sheer output and in a total war the larger economy is going to win eventually.

The biggest strategic mistakes were going to war with the US when they didn't necessarily have to, choosing to fight a 2 front war and continuing to fight Britian when they had no real chance of winning quickly. Really you would need to change all 3 of these for Germany to have any real chance of winning.

2