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Ralsina.Me — Roberto Alsina's website

More on .9999... and 1

Read the com­ments. I am ashamed of math­e­mat­i­cal ed­u­ca­tion, right now. If these peo­ple has passed any math­e­mat­ics tests (and some even claim to have gone to col­lege), maths are hope­less­ly dif­fi­cult.

Some choice quotes:

1/3 is a sym­bol for a set of 4 word­s, it is not a NUM­BER.

On­ly a sin­gle num­ber CAN POS­SI­BLY = 1. Oth­er num­bers may ADD UP to 1, but they don't EQUAL 1. Since 1 clear­ly = 1, .99999 re­peat­ing sim­ply can­not equal 1.

.33(repet­ing) is ir­ra­tional.

.99999 does not equal 1. It might in the CUR­RENT UN­DER­STAND­ING of math­e­mat­ic­s, but that don't make it true.

Math­e­mat­ics can­not even prove that .99999 ... is not equal to 1.

Right now, math re­al­ly can't deal with in­fi­nite num­bers

.9 re­peat­ing, an ir­ra­tional num­ber, is AB­SO­LUTE­LY EQUAL to the ra­tio­nal num­ber 1. Can this be used as proof to show there is no such thing as ir­ra­tional num­ber­s?

I'm half tempt­ed to say there is­n't re­al­ly a right or wrong an­swer

I think I've come to the con­clu­sion that .999... = 1 in the same sense that .333... = 1/3. Which is to say, it does­n't, quite, but we treat it like it does be­cause our dec­i­mal sys­tem has prob­lem­s.

0.9 re­cur­ring does not equal 1. Why? Be­cause it's 0.9 re­cur­ring.

1 = .9 re­peat­ing IF WE WANT IT TO.

This is an ex­ploita­tion of our nu­mer­ic sys­tem, to ar­rive at an out­come that is in­deed very close to be­ing true, but the clos­er it gets to be­ing true the fur­ther away it ac­tu­al­ly is.

2.9 re­peat­ing plus 2.9 re­peat­ing equals 5.9 re­peat­ing 8

And this last one is amaz­ing. The poster pro­pos­es a num­ber that is a 5.9 (an in­fi­nite num­ber of 9s... and an 8). Right. An 8. Af­ter in­fi­nite 9s. At the end of them. Right there. Go to in­fin­i­ty po­si­tion, then one more. There's the 8.

My mind bog­gles. And it's a mind that ac­tu­al­ly ac­cepts .99(re­peat­ing) is 1.

Justin Smith / 2006-11-04 03:47:

let c=.999....
10*c=9.999...
10c-c=9.99999-c
9c=9
c=1
there is your proof it is flawless

Roberto Alsina / 2006-11-04 12:06:

Well, it assumes that 10*.999... is 9.9999...

Which is not the case if you refuse to accept an actual infinity, but hey, I am not in needs of convincing ;-)