∞ is a free variable

[Magnus Anderson]

I can't! That't the fucking problem.

Well, in that case, you can't tell its parity and you certainly claim that it's neither even nor odd.

[Magnus Anderson]

Odd(x in N) -> {True, False}
Even(x in N) -> {True, False}

Classic Skepdickian sophistry.

What you're doing here is you're redefining the terms "even" and "odd". You're turning them into functions. But functions aren't propositions either. So not only are you redefining the terms, you're also doing it in a rather dumb way.

[Skepdick]

Odd(x in N) -> {True, False}
Even(x in N) -> {True, False}

Classic Skepdickian sophistry.

What you're doing here is you're redefining the terms "even" and "odd". You're turning them into functions. But functions aren't propositions either. So not only are you redefining the terms, you're also doing it in a rather dumb way.

I am using standard definitions, imbecille.

Odd(x in N) -> {True, False}
Even(x in N) -> {True, False}

Input: Natural number
Output: True or False.

Code: Select all

In[1]: odd = lambda x: (x % 2) == 1

In [2]: even = lambda x: (x % 2) == 0

In [3]: odd(1)
Out[3]: True

In [4]: even(1)
Out[4]: False

[Skepdick]

Well, in that case, you can't tell its parity and you certainly claim that it's neither even nor odd.

Contradiction. That's precisely what makes it neither odd nor even.

if I could tell its parity it would be either Odd; or Even.

[Magnus Anderson]

I am using standard definitions, imbecille.

Odd(x in N) -> {True, False}
Even(x in N) -> {True, False}

Input: Natural number
Output: True or False.

Code: Select all

In[1]: odd = lambda x: (x % 2) == 1

In [2]: even = lambda x: (x % 2) == 0

In [3]: odd(1)
Out[3]: True

In [4]: even(1)
Out[4]: False

Sorry, you're right. I forgot that you also don't know what a definition is. Adding it to the list.

The words "odd" and "even" do not refer to functions. You treating them as functions is you redefining the terms.

Make that your homework.

[Magnus Anderson]

Well, in that case, you can't tell its parity and you certainly claim that it's neither even nor odd.

Contradiction. That's precisely what makes it neither odd nor even.

if I could tell its parity it would be either Odd; or Even.

So you're just going to stubbornly repeat your infantile bullshit.

[Magnus Anderson]

And functions aren't propositions either, cretin.

The Law of Excluded Middle applies to propositions, not functions.

[Skepdick]

And functions aren't propositions either, cretin.

The Law of Excluded Middle applies to propositions, not functions.

You are out of our depth.

The functions (as implemented in Python) are precisely identical to proofs of the Proposition N -> {Odd, Even}

Propositions ARE types.

https://ncatlab.org/nlab/show/propositions+as+types
https://ncatlab.org/nlab/show/propositi ... neral_idea
https://planetmath.org/111propositionsastypes

[Magnus Anderson]

You are out of our depth.

The functions (as implemented in Python) are precisely identical to proofs of the Proposition N -> {Odd, Even}

Propositions ARE types.

https://ncatlab.org/nlab/show/propositions+as+types
https://ncatlab.org/nlab/show/propositi ... neral_idea
https://planetmath.org/111propositionsastypes

No amount of references can disprove the obvious fact that the words "even" and "odd" do not quality functions just as they do not qualify propositions.

They qualify numbers.

Numbers, functions and propositions are 3 different things.

You playing word games by arbitrarily redefining terms proves nothing.

[Skepdick]

No amount of references can disprove the obvious fact that the words "even" and "odd" do not quality functions just as they do not qualify propositions.

They qualify numbers.

Numbers, functions and propositions are 3 different things.

Being an idiot and being Magnus Anderson aren't two different things...

A proposition is a statement that can be either true or false.

Statements of the form "X is an even number" are propositons.
And so is the computational expression "odd(X)" given the predicate "Odd" defined as follows

Code: Select all

In [1]: odd = lambda x: (x % 2) == 1

In [2]: odd(4)
Out[2]: False

The proposition "4 is odd" expressed using the predicate Odd(4) is false.

You playing word games by arbitrarily redefining terms proves nothing.

It literally proves that Odd(4) is false.

[henry quirk]

I have an off-the-wall, and off-topic, nerd question for Skep and Magnus (anyone can pipe in, though)...

A few days back I was up in the attic, digging thru old boxes. I found an old comic series from '89 called Open Space. The series featured a kind of faster than light tech called a Smoots Drive. This is how the drive worked...

You had a teleporter (mebbe some kind of quantum tunneler) with an effective range of 2 times the Bohr Radius (the width of a single hydrogen atom). This is a hard limit. The teleport cycle, from start to finish, took one unit of whatever the smallest increment of time is (I think that's Planck Time, yeah?). By quickly repeating the teleport cycle an object could be made to move (without actually moving [it remains at relative rest]). Repeat the cycle fast enough and the object could exceed light speed, by a lot.

The drive was described as being small, simple to use, mechanically robust, and very energy efficient. It didn't even need much computer power to operate, only an auto-switch or repeater to keep the cycle going. It's only limit: it only worked in a near vacuum.

As the series focused on the effects of such a drive on individuals and societies, rather than the drive itself, the reader never got much info about the tech beyond what I've described. No upper limit to the drive's pseudo-speed was ever offered. The closest the series ever came to that was in the brief mention it took four days to make a one-way 41 light year trip. But it wasn't explained why.

So, here's the question: ignoring all the impossibilities of such a technology, what would be the upper pseudo-speed limit of such a drive (as I've described it)? I have no clue where to even begin figuring such a thing out. You guys, though, you're math guys, so mebbe you can.

[Skepdick]

I have an off-the-wall, and off-topic, nerd question for Skep and Magnus (anyone can pipe in, though)...

A few days back I was up in the attic, digging thru old boxes. I found an old comic series from '89 called Open Space. The series featured a kind of faster than light tech called a Smoots Drive. This is how the drive worked...

You had a teleporter (mebbe some kind of quantum tunneler) with an effective range of 2 times the Bohr Radius (the width of a single hydrogen atom). This is a hard limit. The teleport cycle, from start to finish, took one unit of whatever the smallest increment of time is (I think that's Planck Time, yeah?). By quickly repeating the teleport cycle an object could be made to move (without actually moving [it remains at relative rest]). Repeat the cycle fast enough and the object could exceed light speed, by a lot.

The drive was described as being small, simple to use, mechanically robust, and very energy efficient. It didn't even need much computer power to operate, only an auto-switch or repeater to keep the cycle going. It's only limit: it only worked in a near vacuum.

As the series focused on the effects of such a drive on individuals and societies, rather than the drive itself, the reader never got much info about the tech beyond what I've described. No upper limit to the drive's pseudo-speed was ever offered. The closest the series ever came to that was in the brief mention it took four days to make a one-way 41 light year trip. But it wasn't explained why.

So, here's the question: ignoring all the impossibilities of such a technology, what would be the upper pseudo-speed limit of such a drive (as I've described it)? I have no clue where to even begin figuring such a thing out. You guys, though, you're math guys, so mebbe you can.

Distance per cycle: 2 * Bohr radius = 2 * (5.29 × 10^-11 m) = 1.058 × 10^-10 m
Time per cycle: 1 Planck time = 5.39 × 10^-44 s
Speed = Distance / Time = (1.058 × 10^-10 m) / (5.39 × 10^-44 s) = 1.96 × 10^33 m/s

About 6.55 × 10^24 times the speed of light.

[henry quirk]

About 6.55 × 10^24 times the speed of light.

Well, that's...fast.

Thanks, Skep.

[AlonsoAcevesMX]

Exploring the connection between numbers and the divine has long fascinated philosophers. Pythagoras believed numbers held the essence of reality, while Plato saw them as eternal and perfect forms. More recently, Carl Sagan's novel Contact pondered the message encoded within the pi constant.
Mathematics is philosophy's first love.