Why do people struggle so much with the idea that .999...=1

[Deleted]

So, not sure if any of you have had this discussion with anyone before, where they are convinced that .999... (point nine repeating) is a number "infinitely close to 1 but not ACTUALLY equal to 1" and no amount of proof will persuade them otherwise.

Like, there are a lot of things out there where it's either a matter of opinion (so can't be proven one way or another) or is something with a provable answer but it's either quite complicated or difficult to prove or whatever, and to an extent it's like understandable that those kinds of thing are going to be difficult to explain to people but with this .999... thing, it's pretty easy to show, so why do people defend it SO strongly? What is it about this specific thing that makes people cling to it so strongly?

Like, when it was first explained to me and I didn't get it, I was ADAMANT that all these things that people were showing me as proof were just wrong somehow and couldn't understand why people were defending it so strongly, and now that I'm like, on the other side of the argument or whatever it's equally frustrating to see people just not accepting clear proof of something, but I still just don't get what it is about this one specific 'argument' that people feel so strongly about?

[Wilian]

Logic dictates that if it's 1, it's 1. But it's 0.999...

[Temp name]

Because people can't fathom infinity.
When I see someone write .999.... I stop thinking past those 3 numbers, and my mind gets stuck thinking it's just that, .999 instead of what it actually is.

At least that's what I think.

[Deleted]

Logic dictates that if it's 1, it's 1. But it's 0.999...

We have no difficulty understanding that, say, 2/2 or 3/3 (two halves, three thirds) are equal to 1 even though 2/2 looks different to 1 though? They hold the same value and that's all that should matter?

[Temp name]

Logic dictates that if it's 1, it's 1. But it's 0.999...

A third of 1 is .3333...
3 times .3333... is .9999....

Ergo, .9999.... is 1

[tratra]

depends what you gonna use it for... its for a forecast for example .999 might come out as 0

Sorry to say that but in science there is nothing proven and everything can equally be disproved.

[Deleted]

depends what you gonna use it for... its for a forecast for example .999 might come out as 0

Sorry to say that but in science there is nothing proven and everything can equally be disproved.

What? It's not science, it's raw maths, where things can be proven.

[Temp name]

depends what you gonna use it for... its for a forecast for example .999 might come out as 0

Sorry to say that but in science there is nothing proven and everything can equally be disproved.

.999 might. .999... isn't .999 though, it's .999 repeating

[Deleted]

Math is man made, man constructed the system so that 0.999... has the same value as 1. Theyre not the same number, they just have the sane value I guess?

[tratra]

What? It's not science, it's raw maths, where things can be proven.

I strongly disagree!

[Slant]

A third of 1 is .3333...
3 times .3333... is .9999....

Ergo, .9999.... is 1

I can't see a mistake in that logic. I thought Erin was trolling us, now I'm not so sure anymore...

[Deleted]

I can't see a mistake in that logic. I thought Erin was trolling us, now I'm not so sure anymore...

No, it's absolutley a thing.




Here's a video with 9.999... reasons why .999...=1

[Slant]

No, it's absolutley a thing.




Here's a video with 9.999... reasons why .999...=1

I looked to my trusted Youtube source for anything numbers... Numberphile, and they agreed with you. Thank you Erin, I learned something new today. So this is a good day!

[Priestiality]

We have no difficulty understanding that, say, 2/2 or 3/3 (two halves, three thirds) are equal to 1 even though 2/2 looks different to 1 though? They hold the same value and that's all that should matter?

1/3 isn't literally .333... It's what's used to represent the concept of 1/3 as decimal number. You're trying to equate concepts humans invented to make calculation easier with real numbers. And when I say "real" numbers I mean the mathematical definition, not "numbers that actually exist".

[Deleted]

I used to try to turn the logic back on itself.

'If it's .999 repeating, so long as it repeats, it can't ever be an integer, and thus isn't 1. As soon as it stops repeating, it is no longer infinite, and thus isn't 1.'

[Deleted]

I strongly disagree!

There's nothing to disagree about. Maths is a constructed world where we define the rules. It's one of the only cases where something CAN be proven with 100% certainty.

[Slant]

I used to try to turn the logic back on itself.

'If it's .999 repeating, so long as it repeats, it can't ever be an integer, and thus isn't 1. As soon as it stops repeating, it is no longer infinite, and thus isn't 1.'

Well, then it wouldn't be .999 repeating and not subject of this discussion, would it?

[Deathquoi]

Is .333... equal to .34? Is .666... equal to .67?

[Vetis]

cant say i've ever met anyone who cared about this at all and I work in IT support, you must know some major nerds.

[Temp name]

1/3 isn't literally .333... It's what's used to represent the concept of 1/3 as decimal number. You're trying to equate concepts humans invented to make calculation easier with real numbers. And when I say "real" numbers I mean the mathematical definition, not "numbers that actually exist".

It is though.. .333... is exactly 1/3. Just like .666... is 2/3, and .999... is 3/3