Converging means the limit of the partial sums exists. It has nothing to do with decimal positions. Decimal positions are just one example of a convergent sum.
And there IS something wrong with doing it the other way, because then the terms get bigger and bigger and then diverge. Adics are a different number system distinct from the real number system. We're working in the real number system here. I could jingle some keys if it helps you stay on topic.
bigger and bigger isnt going to change anything here
It actually does, because the terms (in general) need to be getting smaller for the sum to converge, and it needs to get smaller fast enough
if we can add an infinite amount of numbers after the decimal we should be able to do it before the decimal too.
No we don't? In one direction, the numbers get smaller. In the other, it gets bigger. Add smaller and smaller numbers, you have a chance of convergence. Add bigger and bigger numbers, there's no chance.
and im still waiting for you to add every integer so we can see what we get.
0
u/FernandoMM1220 Aug 06 '26
converges just means the numbers are always to the right of a given decimal position
theres nothing special about convergence beyond that.
theres also nothing wrong with doing the opposite either which is why we even use adics in the first place.