∞ is a free variable

[Skepdick]

Dummy. You are describing floor division. Dummy.

N / N -> N

The remainder doesn't matter.

Well, as I've said a million times by now, you're either severely retarded or you're being paid to destroy thought.

I can't tell which one is worse.

The remainder is there, you moron. That's the entire point. The remainder of 6 div 4 isn't 0 merely because it's not part of the result ( which is your nonsense bullshit meant to disprove the very banal claim that every integer is either even or odd and that there are no integer neither even nor odd. )

It's part of your bullshit against classical logic.

There where, moron?

3/2 = 1

[Magnus Anderson]

There where, moron?

3/2 = 1

It's implicit, fuckface. The remainder is the difference between the dividend ( 3 ) and the divisor ( 2 ) multiplied by the quotient ( 1 ). In other words, it's 3 - 2 x 1 which is 3 - 2 which is quite simply 1. It does not have to be inside the result for it to exist, you moron.

[Skepdick]

There where, moron?

3/2 = 1

It's implicit, fuckface.

Fuckface, that means it's NOT there.

EXPLICIT means it's there.
Implicit means it's in your fucking head.

[Magnus Anderson]

It's like a complete and utter imbecile arguing that there is no such thing as the average height of a population because it's not something that is fully contained within any single member.

What exactly are you doing on a philosophy board, idiot?

You're utterly incapable of abstract thought.

[Skepdick]

It's like a complete and utter imbecile arguing that there is no such thing as the average height of a population because it's not fully contained within any single member.

What exactly are you doing on a philosophy board, idiot?

You're utterly incapable of abstract thought.

You want to talk to an information theorist about statistics ?

What's the average size of the population of natural numbers, Mr Abstract thinker.

[Magnus Anderson]

Fuckface, that means it's NOT there.

EXPLICIT means it's there.
Implicit means it's in your fucking head.

As I said, this guy is severely retarded.

[Magnus Anderson]

You want to talk to an information theorist about statistics ?

What's the average size of the population of natural numbers, Mr Abstract thinker.

Do you ever stay focused, clown?

[Skepdick]

Fuckface, that means it's NOT there.

EXPLICIT means it's there.
Implicit means it's in your fucking head.

As I said, this guy is severely retarded.

Says the idiot who complains about me "destroying thought", then complains about things being made explicit.

implicit
/ɪmˈplɪsɪt/
adjective
1.
suggested though not directly expressed.

explicit
/ɪkˈsplɪsɪt,ɛkˈsplɪsɪt/
adjective
stated clearly and in detail, leaving no room for confusion or doubt.

[Skepdick]

You want to talk to an information theorist about statistics ?

What's the average size of the population of natural numbers, Mr Abstract thinker.

Do you ever stay focused, clown?

Laser focused. For years at a time.

[Skepdick]

It's like a complete and utter imbecile arguing that there is no such thing as the average height of a population because it's not something that is fully contained within any single member.

What exactly are you doing on a philosophy board, idiot?

You're utterly incapable of abstract thought.

Not only am I educating you on abstract thought, I am also educating you on reification.

https://en.wikipedia.org/wiki/Reificati ... r_science)

In computer science, reification is the process by which an abstract idea about a program is turned into an explicit data model or other object created in a programming language. A computable/addressable object—a resource—is created in a system as a proxy for a non computable/addressable object.

[Magnus Anderson]

Says the idiot who complains about me "destroying thought", then complains about things being made explicit.

You're outright lying.

Thought exists and is important precisely because very few things are explicit. You have to subconsciously think to so much as observe anything. You have to deduce what's out there based on whatever immediately surrounds you and interacts with you. You don't just directly observe things that are several feet away from you. You suffer from that very old "direct realism" disease that has infected a lot of so-called thinkers. They all reject it but they still can't fully escape it . . . . still stuck inside of it, mostly unaware of how stuck they are. I don't expect you to understand any of this, you're hopeless, but it's pretty evident to me.

[Magnus Anderson]

Not only am I educating you on abstract thought, I am also educating you on reification.

https://en.wikipedia.org/wiki/Reificati ... r_science)

In computer science, reification is the process by which an abstract idea about a program is turned into an explicit data model or other object created in a programming language. A computable/addressable object—a resource—is created in a system as a proxy for a non computable/addressable object.

You're not educating anyone on anything. You're literally destroying thought and being an extremely arrogant severely retarded dick.

[wtf]

Then I define an odd number as an integer that's not even.

The semantics aside - this step is not constructively valid.

Negation is involutive in a classical setting because Excluded Middle. It's not involutive in a constructive setting.

For this particular instance you need to prove that odd and even are fully exhaustive categories first before you can define an involutive relaton between the "odd" and "even" predicates.

I'd like to understand your reasoning more clearly.

Suppose I make the following definition:

An integer is even if it's divisible by 2.

Here "divisible by 2" has its obvious meaning. The integer is 0 mod 2. Or it has remainder 0 upon integer-division by 2. I hope we don't have to play word games about the meaning of divisible by 2.

Suppose I make the additional definition:

An integer is odd if either

a) It's not divisible by 2; or

b) Its divisible-by-2 status is in some kind of intederminate state.

I have two questions:

1) What's wrong with that definition? A number is odd if it's not even; namely, if it's either definitely not divisible by 2, or else it's in some kind of intuitionistic twilight state.

So I have an "Even machine." I enter a number. If it's divisible by 2, the machine outputs "Even." If it's definitely not divisible by 2, or if the machine can't figure out if it's divisible by 2, it outputs "Odd."

What's wrong with that?

2) I can't believe Brouwer and all the other clever early intuitionists couldn't define an even number. Convince me that this is the correct interpetation, and that you really think I can't define what an even number is without the law of the excluded middle. Can you explain to me how determining if an integer is even could end up in an indeterminate state?

After all, dividing an integer by 2 can be completed by a Turing machine in a finite number of steps. So we can always have a Yes/No machine for the question, "Is n even?" So I just don't understand what an indeterminate answer could be in this context.

[Magnus Anderson]

I hope we don't have to play word games about the meaning of divisible by 2.

Not gonna happen.

[Magnus Anderson]

The set of all integers is { ..., -3, -2, -1, 0, +1, +2, +3, ... }.

The set of all even integers is { ..., -4, -2, 0, +2, +4, ... }.

The set of all odd integers is { ..., -3, -1, +1, +3, ... }.

Can he name a single integer that is neither even nor odd?

Of course he can't -- not without redefining the terms.

His argument so far has been that if you define the term even number as an integer that leaves no remainder when you divide it by 2 using integer ( = Euclidean ) division that it follows that every integer is an even number.

0 div 2 = 0
( no remainder in the result, only quotient that is 0, so 0 is an even number )

1 div 2 = 0
( no remainder in the result, only quotient that is 0, so 1 is an even number )

2 div 2 = 1
( no remainder in the result, only quotient that is 1, so 2 is an even number )

3 div 2 = 1
( no remainder in the result, only quotient that is 1, so 3 is an even number )

And so on.

It's pure sophistry employing equivocation in an effort to construct a seemingly good argument that is in actuality terribly flawed.

The flaw consists in him not really understanding what a remainder is, mistakenly thinking that if a remainder is not included within the result of the division, that it's not there, that it's 0.

At the same time, he has ignored that there are alternative intensional definitions of the term even number, at least two that don't rely on the concept of remainder.

For example, an even number can be defined as an integer that when divided by 2 using real number division results in a number with no fractional part. Alternatively, you can define it in terms of modulo operation.

But we should not worry, I am sure he can construct equally if not more idiotic arguments against these other definitions all with the aim to make it look like he has refuted extremely basic widely accepted beliefs.