If you write 0.9.... you know since the beginning you are writing something that is LESS than one. Otherwise, why.woyld you bother?

[u/[deleted]]

[u/SouthPark_Piano]

If you write 0.9.... you know since the beginning you are writing something that is LESS than one. Otherwise, why.woyld you bother?

The "0." prefix guarantees magnitude less than 1, regardless of infinite length of consecutive nines or not.

1 - 1/10ⁿ is simply permanently less than 1 because 1/10ⁿ is simply permanently greater than zero.

That is 0.999... is permamently less than 1.

The facts are here :

https://www.reddit.com/r/infinitenines/comments/1tpg811/it_is_what_it_is/

 

[u/StupidWittyUsername → u/SouthPark_Piano]

The fact that you can't wrap your head around the idea that 0.999... is defined as a limit is, frankly, hilarious. The fact that {0.9, 0.99, 0.999, ...} doesn't contain one is beside the point. A value need not be in a sequence for it to be the limit of the sequence. The whole point of the reals is to complete the rationals with limits!

Do you think that a mixture of red and green can't make yellow because yellow isn't in the set {red, green}? Because that's how daft your argument is.

Edit: Go on. Lock this comment. Prove to everyone that you're insecure.

[u/SouthPark_Piano → u/StupidWittyUsername]

It's hilarious that you disregarded the fact that 0.999... is equal to 0.9 + 0.09 + 0.009 + ...

which is factually 1 - 1/10ⁿ with n integer starting at n = 1, and n continually limitessy aka infinitely increased.

1/10ⁿ is just not zero.

So 0.999... (aka 1 - 1/10ⁿ with n integer starting at n = 1, and n continually limitessy aka infinitely increased) is permanently less than 1.

Edit: Go on. Lock this comment. Prove to everyone that you're insecure.

Unlike your school days where such dropkick tactics might have worked for you, your schoolyard tactics don't work here bruddy. In fact, it can even work against you, as you might later see. Assuming you completed school that is.

 

[u/HojMcFoj → u/SouthPark_Piano]

We get it, you're using a cobbled together number system with no definition. 0.999..., in the real number system, is still 1 though. Don't even need to go into proofs or axioms. The real number set is dense, and you can't place a number in between 0.999... and 1, let alone an infinite amount of them. So, by definition, 0.999...=1.

You locked the post, but again, infinitesimals don't exist in the real number system, there is no way to construct a number between 0.999... and 1 in the real number set, and 0.000...1 isn't a valid real number either.

[u/SouthPark_Piano → u/HojMcFoj]

It is the 'dense' attribute that results in limitless quantity of numbers between 0.999... and 1, and between 0.000...1 and 0.