Daily reminder that mathematics isn't just True with a capital T. You have to make absurd assumptions about the realm of ideas.
Namely you must assume the existence of an infinite set.
Also reminder that Choice is natural and only breaks because of infinity.
Literally no reason to take infinity on faith.
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You don't have to do anything, you can state all consequences as conditional.
Just adopt some rules of inference in a formalist fashion, and then instead of saying
>axioms A1, A2, A3 make for my theory, and in it, from B, I can prove C
you simply prove
>(A1 and A3 and A3) implies (B implies C)
>Also reminder that choice is natural and only breaks because of infinity.
I agree
Daily reminder that logical disciplines are not about truth, but validity. If you don't understand that you should become an accountant.
>babby's first mathematical philosophical insight
Also,
>2017
>being a platonist
ISHYGDDT
Numbers are infinite, they couldn't exist otherwise (nor could anything).
...
>finitism
Wittgenstein and Wildburger, pls
>You have to make absurd assumptions about the realm of ideas.
There is no transcendent, actually-existing "realm of ideas," only that which is constructed from the assumptions and definitions we make. All "mathematical truth," without exception, relies on assumptions.
Mathematics is "true" in the sense that when you lay out a set of formalized rules for abstract reasoning and symbolic manipulation, and then make a set of unambiguous definitions, what those definitions entail/imply is a priori true, as nothing more than a property of the rule system you're using.
The "realm of ideas" is not some parallel universe which we can observe, over which "sets can be infinite" is somehow a less "empirically valid" assumption than "sets can only have finitely many elements" - because here we have no robust notion at all of empirical truth/observation/evidence. The only "realm of ideas" it even makes sense to talk about is that which follows from the conceived rule sets and definitions
This.
Literally just " 'sets can be infinite' implies X, Y, Z; 'sets must be finite' implies X', Y', Z'." There is no need in the first place to defend any axiomatic system as "more valid."
In fact, it's nonsense to talk about validity of an axiomatic system (relative to this illusory "absolute realm of ideas") at all. The only invalid axioms are invalid through a contradiction they imply within the theory.
The natural numbers are an infinite set of numbers
The set of all shitposts on Veeky Forums is another infinite set.
>The set of all shitposts
I'm afraid it has formed a proper class as of recently.
Atheists are the worst.
5/3 = 1.6 repeating
Done
disproven see
>t. brainlet materialist
Nothing wrong with a system of logic being internally self-consistent. Something doesn't have to be absolutely True for it to be useful.
I had to take a first-year econ course recently for breadth requirements and the professor kept going on about how economics was a "science" because there were "laws" that they stated to be absolutely true. And I was like "dude, that sounds way more like a math than a science to me". Prof hated me for the rest of the course.
But like there's nothing WRONG with economics being a math, just show that your assumptions reasonably hold in reality and you can use economics-as-math to do economics-as-science.
>idealism
>in 2017
spook. plus that only happens depending on the base.
Lol what a retard
Math is absolute
Proof:
Disproof 1+1=2
Define what those symbols and their placement means and why I should believe you.
> 2017
> not a Chad Aristotelian
Lmao
Mathematics is like a skyscraper
the set theorists are concerned that the cobwebs in the basement are of much concern
Infinite doesn't exist. You can prove this by showing that one infinite requires another infinite to exist. For example if you want to count an infinite amount of things it requires an infinite amount of time as well.
Infinity simply doesn't exist in reality. It's an idea, nothing more, like Cthulu.
>all idealism is platonism
Why don't you do what you do and let the actual mathematicians worry about the math
5/3 = 1.666...
1.666... × 2 = 3.333...2
1.6 × 2 = 3.2
1.66 × 2 = 3.32
1.666 × 2 = 3.332
1.6666 × 2 = 3.3332
1.66666 × 2 = 3.33332
1.666666 × 2 = 3.333332
1.6666666 × 2 = 3.3333332
1.66666666 × 2 = 3.33333332
1.666666666 × 2 = 3.333333332
1.6666666666 × 2 = 3.3333333332
1.666...6 × 2 = 3.333...2
1.666...6 ÷ 5 = 0.333...3
0.333...3 × 5 =
0.3 × 5 = 1.5
0.33 × 5 = 1.65
0.333 × 5 = 1.665
0.3333 × 5 = 1.6665
0.33333 × 5 = 1.66665
0.333333 × 5 = 1.666665
0.3333333 × 5 = 1.6666665
0.333... × 5 = 1.666...5
1.666...5 × 2 = 3.333...
0.333... × 3 = 0.999...9
0.333... × 4 = 1.333...2
1.32 ÷ 4 = 0.33
1.332 ÷ 4 = 0.333
1.3332 ÷ 4 = 0.3333
1.33332 ÷ 4 = 0.33333
1.333332 ÷ 4 = 0.333333
1.3333332 ÷ 4 = 0.3333333
1.333...2 ÷ 4 = 0.333...
0.333.. × 3 = 0.999... ≠ 1
1 + 0.333 = 1.333...
1.3 ÷ 4 = 0.325
1.33 ÷ 4 = 0.3325
1.333 ÷ 4 = 0.33325
1.3333 ÷ 4 = 0.333325
1.33333 ÷ 4 = 0.3333325
1.333333 ÷ 4 = 0.33333325
1.3333333 ÷ 4 = 0.333333325
1.333... ÷ 4 = 0.333...25
0.325 × 3 = 0.975
0.3325 × 3 = 0.9975
0.33325 × 3 = 0.99975
0.333325 × 3 = 0.999975
0.3333325 × 3 = 0.9999975
0.33333325 × 3 = 0.99999975
0.333...25 × 3 = 0.999..75
0.333...25 = 1.333... ÷ 4
1.333... = 1 + 0.333...
if 1 = (0.333... × 3)
so no you cant even quantify infinity that way.
>1.666...6 ÷ 5 = 0.333...3
>0.333...3 × 5 = 1.666...5
FUCK
If infinite sets don't exist, what's the largest number?
>isn't just True with a capital T
Why are brainlets always so obsessed with perfection?
>Literally no reason to take infinity on faith.
You don't take it "on faith," you operate from the starting premise where it's true. You don't have to believe something is true to operate from the starting premise where that something is true. Even children aged 8 and older can understand how to work with hypotheticals*, so what's your excuse?
*news.aetna.com
The largest number is the the number of planck lengths on the observable universe. Use of any number greater is sophistry and non-rigorous
>Trying to use details of our observable universe to define aspects of pure mathematics
That's retarded, you're retarded. The whole point of mathematics is it isn't tied to details of the physical world. It's pure abstraction, what our world is like has no relevance to it. If you want to deal with how the physical world behaves, go work on physics.
Sophist.
as retarded as the post you replied to is, mathematics comes out of our observations first and foremost.
New methods have suddenly expanded what is considered "the observable universe" all your math is null and void, congrats finitecuck.
>mathematics comes out of our observations first and foremost
First and irrelevantly so, yes. Foremost, no.
Just because we necessarily observed the world first before discovering pure abstract objects and relationships doesn't mean observation is more important than pure abstract objects and relationships. It just means we're limited physical organisms and that was our limited way of getting started. It's completely without relevance to mathematics what historical particulars led into our own discovery of it.
This is, again, the entire point of what mathematics is about. You DON'T tie it to the physical world, you DON'T make it change based on the particulars of physical phenomena in our world. It's a pure system that you can *apply* to the physical world if you want, but that's the same thing as saying the system itself is a study of the physical world.
This. What - historically motivated - the development of mathematics says nothing at all about what ontological category it falls into, and saying otherwise is a category mistake.
Science is about empirically derived models with predictive capability. Why does it use math? To be exactingly precise with the testable predictions a model makes. In math - itself - all things which are true follow from the axioms and definitions we establish. This clearly stands at odds with science, which makes no pretense towards "absolute truth," only towards successively better models for describing and predicting the material world. They're totally different ontological entities, and pointing this out isn't "sophistry."
Science adopts math to clarify its claims precisely because every true fact in math is true a priori (where it is understood which system we are working with.) This allows a simple, readable list of premises, like the postulates of QM, to unambiguously imply the broad whole of a theory's scope and claims. Then the only concern is with the theory's correspondence to reality, and not with endless and contradictory "reinterpretations" of the theory itself
"Sometimes we try to be precise and concise with what we're claiming" =/= "The universe is math, dude!"
We need base-18 to handle repeating decimals so people dont think "1•••" is actually treated like either "1" or many "1"s. Repeating infinite sets should be seen as completely unique numbers since these repetitions often defy understanding of finite arithmetic.
For example:
3 × 4 = 12
0.3 × 4 = 1.2
0.33 × 4 = 1.32
0.333 × 4 = 1.332
0.3333 × 4 = 1.3332
0.33333 × 4 = 1.33332
0.333333 × 4 = 1.333332
you can see a pattern emerge where, if continued infinitely, you mighy expect:
0.333•••3 × 4 = 1.333•••2, where the subfinal significand attempts to have the sane meaning derived from normal finite arithmeric, yet ultimately does not.
To make clear that 0.3333333333333333333333333333333 and 0.3••• are entirely different numbers requires the repetition symbology of the latter to be redefined.
A base-18 system could be used to achieve this, written:
01a2b3c4d5e6f7g8h9
the repetition property could be taught as
0》1》2》3》4》5》6》7》8》9
》》a》b》c》d》e》f 》g》h》》
Where the intermediary numbers are treated like black notes on a piano.
Using this setup, a problem such as
0.333••• × 3 = 0.999••• = 1, would instead more easily be understood as
0.c × 3 = 1
In that we understand c to be the intermediary representation of 3, so if we count (3×3=) 9 on the intermediary number line we get
abc def gh1
Employed in binary would require 5 digits to cover the system
00000 = 0
00001 = 1
00010 = a
00011 = 2
00100 = b
00101 = 3
00110 = c
00111 = 4
01000 = d
01001 = 5
01010 = e
01011 = 6
01100 = f
01101 = 7
01110 = g
01111 = 8
10000 = h
10001 = 9
Where 0-9 are
>00000 = 0
>00001 = 1
>00011 = 2
>00101 = 3
>00111 = 4
>01001 = 5
>01011 = 6
>01101 = 7
>01111 = 8
>10001 = 9
which can be manipulated pretty easily, just as a-h
>00010 a
>00100 b
>00110 c
>01000 d
>01010 e
>01100 f
>01110 g
>10000 h