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Continuation of this dead is ".999...=1?"...
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Continuation of this dead is ".999...=1?" thread. His arguments I respond to are in pic. I hope OP is still on /b/.

OP argued that it his argument, .999...converges to 1, and therefore there will always be a small difference between .99... and 1. I have two separate arguments.

1. Define t(n)=1-s(n) = {.1,.01,.001,...}
Now for n=infinity where t(n)= .000...1, let us consider 1-t(n). When subtracting, we subtract from left to right.
That is, we subtract:
1.0-0
1.00-.00
and so forth. We would obtain 1.00... by definition of infinity. It is true for .0000...1 that there is a 1 at the end, but you don't get there because the string of 0's is infinite. It's like how (infinity + 1) is not a possible number.

The difference does exist on an infinitesimal scale, but it has no effect in finite calculations. In other words, I think this infinitesimal difference would only be significant in infinite calculations, but not in the finite field.

But this also "converges" to zero:
.9999...-.9=.0999...
.9999...-.99=.0099...
.9999...-.999=.0009...

I think because your main argument is that "convergence it not equality," to argue .999... is not equal to 1, you'd also have to argue s(n)-s(n) is not equal to zero.
>>
yawn, more brain-jerk, find something productive to do with your life son
>>
.99999... =/= 1

Just look at the numbers. .999... isn't 1 and 1 isn't .999... It's pretty fucking simple
>>
>>546403882
>productive to do with your life
like pic related? That was a great read.

>>546404171
1/4 is not .25 either. Jesus Christ they don't have a single number in common
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>>546404361
Yes they are. That's like saying 2+2=/=4. You have to finish the division
>>
>>546404598
ok, then consider:

x = 0.9999...
10x = 9.9999...
then 10x - x = 9
9x = 9
x = 1
>>
>>546404859
>then 10x - x = 9
No it doesn't
It's 8.9999...
>>
>>546402789

>I would love to have an epiphany that sets me in line with the mathematics community.

Here's one:
>Equivalence ? identity

.999... is equivalent to one, it is not identical to it.
>>
>>546405619
>8.9999...
How'd you get that? It works like:
9.999...
- 0.999...
---------------
9.000...

>>546405861
identity =/= identical
For example, (x + y)^2 and [x^2+2xy+y2] are identities.
>>
1 - 0.99999... clearly has zeros in each decimal place to the right of the decimal point.

Thus 1-0.9999.... = 0.
>>
>>546406464

>identity =/= identical

Semantics

My point was that the numeric concept (cf. the arbitrary character representation)of .999[...] is equivalent with, but not identical to the numeric concept of 1.

So if OP is saying that .999[...] converges to 1 and therefore that it is always not quite 1, then he is correct, but this much is already assumed in the sentence '.999[...] = 1' in the first place.

That's where the whole argument stems from to the point where both sides are arguing the same thing without even realising, but that, since the mathematical community relies upon accepted terminology (who's etymology/creation is not necessarily entirely understood by every mathematician), it will always naturally be in the right. The mistake OP is making is the common mistake that, in mathematics, equivalence is synonymous with identity, or isomorphism. This is a beginner's mistake common enough even so to the point where some amateur mathematicians may actually argue with OP as they themselves are not aware of this distinction.

In fact, being as how the interchangeability of equivalence and isomorphism is ubiquitous in most mathematics, the only people who are really forced to learn of the distinction are those who broach the subject of the philosophy of mathematics. For the rest, the interchangeability between equivalence and isomorphism, or identity, is sufficient.
>>
>...9

There's your mistake. It doesn't end.
Whoever made that image is a retard.
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>>546407417
>common mistake that, in mathematics, equivalence is synonymous with identity, or isomorphism
OP's argues convergence is not the came as equivalence. He's doesn't claim ".999... is not identical to one, and therefore not equivalent."

Also, just curios, would you mind explaining isomorphism in layman's terms? I wikied it and only found a technical explanation.
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>>546402789
aah when will this argument end?
OP, 0.999 is by convention accepted to be equal to 1 in the real numbers system.
that is because nonzero infinitesimals don't exist in real numbers

however, this is true ONLY BY CONVENTION, in alternative number systems that accept nonzero infinitesimals, 1 =/= 0.999... can very well be.

there's even a fucking wiki page about the subject
https://en.wikipedia.org/wiki/0.999...

see especially:
https://en.wikipedia.org/wiki/0.999...#In_alternative_number_systems
>>
>>546409215
>Thinks OP of picture and post are 1) same 2) arguing same side
You either did not read or understand the arguments
>>
>>546409215
Also, CONVENTION is a faggot's argument. It used to be CONVENTION that the earth was flat.
>>
>>546408687
iso - same
morphism - shape

It means that two things can't be rearranged into each other.

The opposite is homeomorphism, for instance a donut can be changed into a cup is a famous example.
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>>546410303
>iso - same
iso - different *
oops
>>
>>546410127
this is irrelevant to what i wrote

>>546410260
>Also, CONVENTION is a faggot's argument
fucking hell, yeah
that's what i was TRYING 3TO EXPLAIN in my post.
did you even read it up to the end?
>>
Inb4 People assuming that .333.... is in any way an accurate representation of 1/3
>>
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saging this shit

1 = 1, this is not your "1 converges to 1" shit. times 3

3 = 1 + 1 + 1, divides by 3

1 = 1/3 + 1/3 + 1/3

1 = 0,333... + 0,333... + 0,333...

idiot.
>>
>>546402789
numbers are made up by man to try to get ahold of the non living
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>>546410373

No you were right the first time. Iso comes from attic greek ???? meaning 'equal'.
>>
>>546410385
>this is irrelevant
No no, understanding words is very relevant in a conversation.

>did you even read it up to the end?
I did read it to the end. That's why I think you're a fag. Pic's OP was asking why people agree .999...=1. In other words, he's asking what proofs/philosophies led people accept that as convention. Then you come along:
>OP: Why is this the convention?
>You: Because it is convention.

You respond to this
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>>546410373
iso does not mean different it means equal
>>
>>546410303
>it means that two things cannot be rearranged
How does that work with numbers? Can you can re-arrange 1/4 into .25? If so, isn't equivalence equivalent to isomorphism? If not, isn't isomorphism irrelevent to OP's claims?
>>
1=1
3/3 = 1
1/3 + 1/3 + 1/3 =1
1/3 = 0.3333333...
0.33333... + 0.33333... + 0.33333... = 1
>>
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>>546412014
circular argument
>>
>>546402789

If .999.... and 1 are different, they must represent different points on a number line, and there must then be infinitely many other numbers between them.

Can anyone name one number that exists between them?
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>>546412148
x=0.9999...
10x=9.9999...
10x - x = 9.9999... - 0.9999... = 9
9x = 9
x = 1
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>>546412518
qed
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>>546412518
actually can you prove 10x=9.9999 ?