That means that 0.99999... is the limit of a_n as n goes to infinity, which is the limit of the above sum, which is a geometric series that simply converges to 1.
Eg: Your answer is .99999 Let x=.99999 Therefore 10x=9.9999 Consequently 10x-x= 9x 9x=9 x=1 I had always assumed that there was a catch to that logic and that it wasn't actually equal to 1, but was approximately equal to or some other mathematical loophole in logic; because surely it couldn't be true. You are right to be suspicious here.
The result of the calculation doesn't depend on how you write it, so 0.99999... and 1 have to be precisely the same result, just written down differently.
In awe of this. Could someone please further explain. I know it has to do with the fact that since 0.99999… converges to 1 through limits but some more mathematical clarification would be appreciated! : r/mathematics Go to mathematics r/mathematics r/mathematics
Hi everyone, I am having trouble understanding what I need to do to make console command "campaign.add_skill_xp_to_hero [SkillName] [PositiveNumber] [HeroName]" work for me... I am following this exact same logic, so I am typing "campaign.add_skill_xp_to_hero One Handed 50000 Salvatore Bitterdraught", but I get a message in the console "Hero is not found". I have tried to use this companion to ...
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1 - .99999 = .00001 As a matter of precision, however far you take this pattern, the difference between 1 and a bunch of 9s will be a bunch of 0s ending with a 1. As we do this thousands and billions of times, and infinitely, the difference keeps getting smaller but never 0, right? You can always sample with greater precision and find a difference?
The general statement you have proven is actually quite interesting You can make any N-digit sequence repeat forever by dividing it by 10 N -1 12345/99999 = 0.123451234512345...
