If 0.999... = 1 then [0,1) has an upper bound of 1...

if 0.999... = 1 then [0,1) has an upper bound of 1, but we all know that 1 is not included in this set yet the set contains 0.999...

How do mathematicians reconcile this contradiction?

>How do mathematicians reconcile this contradiction?
They make new math that fits for the particular inconvenience

>yet the set contains 0.999...
No

What's the upper bound of the set?

the upper bound of the set is 0.999... which is equal to 1. this element is not in the set.

if 0.99999... is equal to one then its not included to the set. An open set means you can get infinitely close to 0.99999.... but not reach it, so there is no contradiction. There is a difference when something tends to infinity and when something is infinity because infinity is a point my man

[math]0.999\dots[/math] is not in the set. By the definition of an open interval, this would mean that [math]0.999\dots < 1[/math], equivalently there exists some (actually infinitely many) [math]x \in \mathbb{R}[/math] such that [math] 0.999\dots < x < 1[/math]. Name one such [math]x[/math].

>there is a difference when something tends to infinity and when something is infinity

semantics, both are infinity.

Proof that the set does not contain 0.999...
I am pretty confident you wont be able to

So many of these fucking threads would be avoided if you fucking idiots knew how to construct the reals
Tell me what a real number is
Go ahead, I'm waiting

any point on the numberline.

made me rage, thanks

No its not. This about it using limits. In like 1/x the value is not defined at 0. You can get infinitely close to 0 but depending on which side you approach you get plus or minus infinity

What about that description made you rage?

It's literally true.

0.99999... is equal to 1 thus it's not included in the set.
Only the finite amount of 9s are in the set

It's the completion of the rational numbers but I have no clue what I'm talking about

t. CS Msc

Then what is the upper bound of numbers within the set, you fucking moron?
No, it means you can go infinitely close to 1, which is .999...
fucktard

>if 0.999... = 1
It is.

>then [0,1) has an upper bound of 1,
It does.

>but we all know that 1 is not included in this set
Indeed.

>yet the set contains 0.999...
No, it doesn't.

>How do mathematicians reconcile this contradiction?
There is none.

>Then what is the upper bound of numbers within the set, you fucking moron?
y'all know that supremum =/= maximum, right?

>No, it means you can go infinitely close to 1, which is .999...
Describe an infinitely small number (the alleged difference), and tell me why there wouldn't be an infinitely smaller number if I just divided that number by 2.

right open intervals don't have upper bounds.

If it had an upper bound you could simply state what it is, for example, the upper bound of [0,5] is 5 because the interval is right closed.

>right open intervals don't have upper bounds.
Yes they do. (Unless they are unbounded on the right side, like (7 - infinity).) An upper bound of a set is any number larger than any number in that set. Upper bounds of [0, 1) include 1, 17, and the length of my dick in centimeters.

The *least* upper bound of a set is the smallest upper bound of the set. The last upper bound of [0, 1) is 1.

The *maximum* of a set is the largest number in that set, i.e. the member of that set (if any) that is larger than all other numbers. [0, 1) does not have a maximum. As you say, [0, 5] has 5 as a maximum.

None of this causes contradiction with the stuff in OP.

Thank you for explaining to this brainlets the basic definition of upper bound.

You left out the part where every1 here including you just brutally gang raped ur mom. And how she gave us money after. Before I set the nasty who're on fire. Her soul is cleansed now.

It doesn't have one...

0.99999... is not in the set [0,1) because you can't put a finitely sized ball around it that contains only values in the set. This also implies its equality to 1.

Holy shit Veeky Forums is bad at math.

>[0,1) = 1
>[0,1] = 1
>[0,1) = [0,1]
>[0,1] - [0,1) = 1
>0 = 1

congratulations on revealing your retardation

Aaaaaahhh shit. bout to get good up in this bitch

0 never = 1
But sometimes 1 can = 0

Just ask ur dad to explain in math what you being born did to his life.

Ur wellkum bye the hwey

Just what the FUCK do you think an upper bound is?