My friend who I am arguing with 9and the whole reason I posted, to try and convince him) is still not convinced that 0.33333…=1
After seeing the post, he said:
[quote]
Hi. Have looked atthe linkvery briefly. First comment on “erislover” - 1/3+1/3+1/3=1/1=1
This is totally foolish because it is based on everybody accepting that 1/3=0.333…which is the actual problem. His whole way of trying to clear this up is to me very unscientific and illustrates the problem with getting info from the web.
This: [But the truth of it, without calculus, is the method you show: .333… is just a representation of one-third.] THIS is the whole problem, I say that this is an insufficient representation of one-third for theoretical math.
[end quote]
BUNK!!! B-U-N-K, BUNK!
Help me correct this guy!
please!
TJ
I only posted this in GD as it was already a closed thread in GQ- but I need more ammo to shoot down my friend!
As Telemark hints, you probably meant to gather arguments that 0.9… is equal to 1, not 0.3… Either that, or you’re impishly writing your numbers in base 4 without telling us.
Many threads on this board have addressed the topic before — although, having only a “Guest” account, you might not have access to the search feature so as to find them all. Two decent Web pages though can be found here and here. Google on “0.999 = 1” and you’ll find a bunch more.
The real challenge isn’t to prove that 0.9… = 1. The challenge is to count how many ways there are of proving it.
In base 4, .3… = 1. In base 5, .4… = 1. In base 16, .F… = 1.
The reason is quite simple. 0.a[sub]1[/sub]a[sub]2[/sub]a[sub]3[/sub]…[sub]R[/sub] is defined to be the series whose nth term is given by a[sub]n[/sub]/R[sup]n[/sup]. With a[sub]i[/sub] = 1 for all i, this can be shown to converge (by means that you can find in an algebra 2 textbook) to 1.
Your friend seems to think that a decimal representation is a matter of opinion or an alternate theory or some such. He doesn’t seem to get it that .333… is – by its very definition – one third. If he can’t get that very basic definition, I see no reason to multiply anything by 3. He refuses the premise, and that’s where you have to convince him.