I was thinking about x=0.999.. so 10x=9.999... therefore 10x-x=9 when I asked myself does the distributive property apply to an infinite number of terms since 0.9999....= sum(9/10^(-k), k=1,2...)? Maybe I'm confused about what "=" means.
Zurtex said:It is of course wrong to assume the distributive property applies to an infinite number of terms. Once you however learn the maths to prove it, you'll find in fact it does (under more strict cirumstances).
This topic has been beaten to death at least a few dozen times on this forum, I remember one thread that went on for over 400 posts.Night Owl said:I thought this topic was beaten to death.
cronxeh said:oH you wont believe just where I've found it :rofl:
On catholics forums! :rofl:
Here you can either use their link or mine:
Speaking of distributive properties:
1 = 0.999.. can be represented as:
So when you multiply by 10 it makes perfect sense since you can divide or multiply the Sum by any number, therefore both multiplication and division will hold for distributive property
All real numbers are represented in infinite form, e.g:pallidin said:Hey, I have a new number system. Ok. probably not new.
Anyway, here it goes:
Instead of 1,2,3,4, etc..., it should be .999~, 1.999~, 2.999~, etc..
And .5 should be .4999~
What my theory posits is that any number can not be an absolute quantity, rather that is must be held in an infinite form.
Would that be when one wants to fit it on the page? Or perhaps when one is a silly physicist and can't get their head round the real number line?Hurkyl said:There are times when one prefers to define the decimals in such a way that a decimal cannot end in an infinite string of zeroes. Or, to define it so that a decimal cannot end in an infinite string of nines.
Hurkyl said:There are times when one prefers to define the decimals in such a way that a decimal cannot end in an infinite string of zeroes. Or, to define it so that a decimal cannot end in an infinite string of nines.