Comment on Panik
Lmao how about …99999 = -1?
This one has always bothered me a bit because …999999 is the same as infinity, so it’s like you’re just doing math using infinity as a real quantity which we all know is invalid.
Yes, you’re right this doesn’t work for real numbers.
It does however work for 10-adic numbers which are not real numbers. They’re part of a different number system where this is allowed.
You can also prove it a different way if you allow the use of the formula for finding the limit if a geometric series on a non-convergent series.
Sum(ar^n, n=0, inf) = a/(1-r)
So …999999 = 9 + 90 + 900 + 9000… = 9x10^0 + 9x10^1 + 9x10^2 + 9x10^3… = Sum(9x10^n, n=0, inf) = 9/(1-10) = -1
But why would you allow it?
Because you could argue that the series does converge to …999999
ledtasso@lemmy.world 2 years ago
This one has always bothered me a bit because …999999 is the same as infinity, so it’s like you’re just doing math using infinity as a real quantity which we all know is invalid.
yetAnotherUser@feddit.de 2 years ago
Yes, you’re right this doesn’t work for real numbers.
It does however work for 10-adic numbers which are not real numbers. They’re part of a different number system where this is allowed.
Snazz@lemmy.world 2 years ago
You can also prove it a different way if you allow the use of the formula for finding the limit if a geometric series on a non-convergent series.
Sum(ar^n, n=0, inf) = a/(1-r)
So …999999 = 9 + 90 + 900 + 9000… = 9x10^0 + 9x10^1 + 9x10^2 + 9x10^3… = Sum(9x10^n, n=0, inf) = 9/(1-10) = -1
Kruemel@feddit.de 2 years ago
But why would you allow it?
Snazz@lemmy.world 2 years ago
Because you could argue that the series does converge to …999999