Philosophy Now Forum

Last prod. Is the infinitary process sufficient for getting from algebraic -> transcendental, or is the fixed point (x - x = 0) also necessary? The algebraic numbers are closed under addition and multiplication (and their inverses). But it's certainly possible for a finite linear combination of tra...

I don't know what you mean by "construct" in this context. If x is transcendental then x - x = 0 is algebraic. So you have to be careful to say exactly what you mean. Lets try. Can I produce some algorithm/computable function which (given infinite time) and using ONLY the set of ALL Algeb...

Yes. That's what makes it algebraic, by definition. And since pi is transcendental -- NOT the solution to any polynomial having integer coefficients -- your equality is false. What I am reading into your sentence (by way of implication) is that there is no way to construct a transcendental number f...

nothing wrote: ↑Sun Feb 09, 2020 4:53 pm However Φ is a real solution to a quadratic equation.

Yes. That's what makes it algebraic, by definition. And since pi is transcendental -- NOT the solution to any polynomial having integer coefficients -- your equality is false.

nothing wrote: ↑Sat Feb 08, 2020 2:42 pm thus
Φ² = Φ + 2π

This cannot be since Φ² - Φ is algebraic and 2π is transcendental.

That's why Skepdick (Logik, Univalence, Timeseeker) presents us with a baffling psychological mistery, how can someone literally not understand anything. Provided that he isn't a chatbot, but he doesn't seem to be one. Skepdick is Logik. Duh!! All is clear now. I can be so naive sometimes. Thanks.

Is n in the definiton of limit is finite? If yes, we are dealing with discrete regime. I am wondering how you could have continuous regime when you are in discrete regime!? You are repeating yourself. I met you more than halfway in trying to understand your point. I agree that there is a very long ...

ps -- I think what you're getting at is that calculus is a brilliant formalism for approaching the continuous from the realm of the discrete. And maybe the question is, what's really going on? This is a very old question. In Newton's time people thought in terms of infinitesimals but it was very con...

If the integral is the area under the curve and the derivative is the tangent of a curve at a given point then integral and derivative are continuous concepts. Yes, that's the freshman calculus point of view. But there are more abstract and general viewpoints on integrals and derivatives that exten...

Integral and derivative are continuous concepts. Even that's not true. For integrals, consider a finite sum is a special case of an integral, as in for example the case of an integral with respect to counting measure. For derivatives, consider the calculus of finite differences. https://math.stacke...

The continuous regime is defined as the limit of the discrete regime when 1/N (infinitesimal) tends to zero (or N tends to infinity). N tends to infinity but never becomes infinity, so it is finite. But we are in the discrete regime when N is finite. So either the definition of the continuous regim...

Skepdick wrote: ↑Sat Nov 30, 2019 8:49 am Duh! All forms of language are "just symbols". Until interpreted by something or somebody they have no inherent meaning.

At the risk of once again feeling like a fool for thinking there is rational dialog to be had with you: Isn't this point exactly what I'm trying to explain to you?

The fact that you actually can't tell the difference between Strings and Integers (or characters and digits) is precisely the bug in your Mathematical brain. The distinction is completely arbitrary and is implemented by the writers of the interpreter. It's not God-given or fundamental in any way. Y...

Strings are not Integers. Neither in Python (interpreted language) nor in C++ (compiled language). Completely missing the point of what I wrote. Missing every aspect, nuance, and subtlety of what I wrote, at every level of meaning . A display of obliviousness that literally precludes intelligent co...

https://repl.it/repls/BraveBlankEvaluations print('0000' == 1) # => False print(len('0000')) # => 4 print(type('0000')) # => <class 'str'> print(type(1)) # => <class 'int'> This shows an astonishing lack of understanding. Surely you know that Python is an interpreted language. That means that when ...