Let's say I have this number: >0.999... + 0.5 0.999...

>>8436201
mathematics CANNOT answer this
it is proof of its INCONSISTENCY

up.

hope this helped.

Occams razor, unless you're doing some weird stats thing where the rules are-clear cut (aka ALWAYS round down in this case to prevent personal interpretation and inconsistances in the data akin to significant figures)

Its obviously "closer" to 1.5. So, up.

>>8436232
So the layman definition of "always round down if your number is followed by 0, 1, 2, 3, 4 and up if 5, 6, 7, 8, 9" is not entirely true?

What is the proper mathematical rule/definition for how/when something should be rounded up or down?

>>8436242
you make easy difficult.
do layman rule. what is last digit of 1.499...? there is no last digit. so you turn 1.499... to 1.5 and then round up

>>8436242
Its entirely logical that that figure is approaches 1.5. So for all intents and purposes, you can consider it 1.5, but if you wanna be extremely accurate, put a * next to it to signify that it is not exactly 1.5. Its the Lim as 0--->1.5 I guess. Perhaps my notation is incorrect but it approaches 1.5.

If your teacher/professor rejects this reasoning, dispute it.

>>8436201
Because 0.999... = 1 and your sum of 1 + 0.5 = 1.5, you round up.
There is no dispute. 0.999... = 1.

If it is a finite sequence of 9s round down, if it is an infinite sequence round up.

You do not round up nor down. 0.999... + 0.5 is equivalent to 1 + 0.5 or 1.4(999...) = 1.4 + 0.1

>>8436201
0.99999... +(1 - 0.99999...) = 1
1 can never be 0.99999...
>American education

>>8436218

Fuck off you cuck.

|0,9999999999999..... | = |1| and both of them are non negative so 0.999999....... = 1

>>8436353
>he doesn't understand the question

>>8436563

1 + (1 - 1) = 1

you prove nothing

Use banker's rounding, problem averted.

>>8436623
Explain how 0.9999999=1?

>>8436282
you only round up once mate

>>8436201
1.5 = 1.4999...
Every post that doesn't point this out is dipshit retarded. Now you know how many idiots are on sci.

>>8436689
0.999999 =/= 1
0.9999.. = 1

Many ways to prove that.
One of them is the following :
x=0.99...
10x = 9.99..
9x = 10x-x = 9
Therefore x=1.

Or else, you could just calculate the limit of sum...

x=.3333..
10x = 3.3333....
9x = 3
x = 1/3
Holy fuck the above method works. Delet this

Can someone redpill me on the axiom of choice? I'm in Calc II but this seems interesting

>>8436201
Assuming this isn't the shitty bait it looks like:
>Technically, it's 1.499..., so it should be rounded down
This is false. You round down number less than 1.5, but 1.499... = 1.5. 1.499... is not less than 1.5, so it is rounded up.

How many significant figures am I rounding to?
If I was rounding to 1 figure, the answer is 1.
Two? 1.5
Three? 1.50
Four? 1.500
To infinity? 1.5000...
The digit right of your uncertainty gets the boot up or down.

>>8436201
>as with all numbers followed by 4
There is your problem. Rounding doesn't say jack shit about "numbers being followed by 4". It's very simple. You round to whichever is closer, if they're equidistant then people usually say to round up. In which case it's two, because 1.4999... = 1.5.

>>8436689
Every two distinct real numbers has an infinite amount of real numbers between them. Name just one that is between .999... and 1.

>>8436915
This, for all practical purposes, has literally nothing to do with the axiom of choice.

>>8436201
>Technically, it's 1.499
Which is the exactly the same number as 1.5. Round up

>0.999... + 0.5

You have only 1 sig fig. Round down to 1.

ffs
Why poeple keep trying to use infinite when they dont understand it ?
Why the fuck infinite sequence of 9 would make 1

the bait is just too damn huge

>>8437613
nice b8 m8

that depends, how many 9's deep are we?