the ultimate question: does 0.9999... equal 1

[SetGaming]

there has been an ultimate for years and months and years of mathematics, and that is: does 0.999, going on until infinity, equal the ultimate universal number of: "1"

can blockland forums bring an ultimatum to this daunting and incredible question???

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[Whackin]

no because its 0.9999... not 1 unless your rounding in that case sure

[Doughboy]

yes.

[FelipeO_O_]

no because 0.999.. equals 0.999..

[Steve5451²]

no. in computing that small difference can mean a lot of problems.

[Ringabel]

scientifically yes
if ur not a frickin nerd no

[Drydess]

on the other hand, does 9999... equal infinity

[EcstaticEggplant]

0.9 recurring does equal 1, it can be proved pretty easily.

[Aide33]

no because 0.999.. equals 0.999..

you must not believe in calculus then

[PhantOS]

x = 0.9999....

multiply both sides by 10

10x = 9.9999...

logic

10x = 9 + 0.9999...

in order for this to be true, x needs to equal 1

10 (1) = 9 + (1)

so 0.9999 is 1

[PhantOS]

also any number less than 9 as the numerator in a fraction over 9 will be equal to 0.xxxxx or whatever that number is right

so 8/9 = 0.888888...

9/9 would not equal 0.999... but actually 1 because any number over itself is always 1

[Maxwell.]

you must not believe in calculus then

do you mind elaborating on that cause I'm genuinely curious

[Crazy Salt]

1/3 = 0.333....
1/3 + 1/3 + 1/3 = 0.999....

1/3 + 1/3 + 1/3 = 3/3 = 1

0.999... = 1

[Mega-Bear]

In calculus when dealing with a limit at 1, it is appropriate to sometimes treat 0.9999... as 1 because a function can get infinitely close to 1, but as long as that limit's there, it will never fully achieve 1. But we still need to occasionally do work with 1, so we substitute 0.9999... instead.

However if we look at this from a chaotician's perspective, differences in starting conditions may lead to enormous differences in a system farther down the line, (source: Jurassic Park) therefore treating 0.9999... and 1 as equal can be dangerous.

It is all about context.

[Maxwell.]

In calculus when dealing with a limit at 1, it is appropriate to sometimes treat 0.9999... as 1 because a function can get infinitely close to 1, but as long as that limit's there, it will never fully achieve 1. But we still need to occasionally do work with 1, so we substitute 0.9999... instead.

However if we look at this from a chaotician's perspective, differences in starting conditions may lead to enormous differences in a system farther down the line, (source: Jurassic Park) therefore treating 0.9999... and 1 as equal can be dangerous.

It is all about context.

that makes sense

1/3 = 0.333....
1/3 + 1/3 + 1/3 = 0.999....

1/3 + 1/3 + 1/3 = 3/3 = 1

0.999... = 1

this is wrong though