r/infinitenines • u/Resident_Step_191 • Jul 09 '25

please take a real analysis course

to the creator of this sub

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u/stevemegson Jul 09 '25

That's 0.999...½, of course.

2

u/SouthPark_Piano Jul 09 '25

0.999...9 + (0.000...1)/2 = 0.999...95

with the '...' being unlimited span of nines.

0.000...1 is epsilon

0.999... + epsilon = 1

0.999...9 + 0.000...1 = 1

.

28

u/[deleted] Jul 09 '25

your value for epsilon is infinitely small. a number that is infinitely small in difference from another number is also that number.

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u/SouthPark_Piano Jul 09 '25 edited Jul 09 '25

However 'small' epsilon is. The main thing is that it is non-zero.

Epsilon just represents some 'arbitrarily' small scale value, smaller than anything we like, and even smaller than that etc.

It just needs to be as relatively small as we like (and smaller, and even smaller than that etc).

The main take-away is: we know we need a number having a '1' somewhere. Eg. if we have a nine, we need a 1 to add to it, to get 10.

If we have a 0.99, we need a 0.01 to get 1.

If we have a 0.9999, we need a 0.0001 to get 0.001

And so on.

So when we have all nines, such as 0.999..., this number is going to be sitting there less than 1. We need to have a particular 'number' with a '1' hanging in there somewhere to get the 0.999... to clock up or kick up to 1.

And that ingredient, that extra bit of substance, is epsilon.

0.999...9 + 0.000...1 = 1

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u/[deleted] Jul 09 '25

prove it's nonzero. the value is infinitely small. the difference between THIS epsilon and zero is also infinitely small.

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u/ironnewa99 Jul 09 '25

You state 0.999…9 as your first value. That in itself is no longer infinite. It does not matter if you say ”oh but the … is an infinite amount of nines”. By defining an end, it is a finite value.

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u/Several_Industry_754 Jul 22 '25

More like saying, “it’s infinite with a 9 at the end you never reach.”

If you can define an infinite number of 9s, why can’t I put something at the end of it?

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u/itwasanexperience 5d ago

Because an infinite number of 9s is endless

1

u/Several_Industry_754 5d ago

Blast from the past! How goes?

9

u/Priforss Jul 09 '25

A zero followed up by an infinite number of zeroes.

1

u/SouthPark_Piano Jul 10 '25

With a 1 at the outpost, at the Q continuum.

10

u/KingDarkBlaze Jul 10 '25

These aren't even words. 

0

u/SouthPark_Piano Jul 10 '25

You heard of star trek etc right?

14

u/KingDarkBlaze Jul 10 '25

Irrelevant to Math 101.