does that mean that there are infinitely infinite infinitely infinite infinitely infinite infinitely infinite infinitely… (etc.) infinities? — an-salad
if there are infinite whole numbers, and there are infinite decimals between 0 and 1, and there are infinite decimals between 0.1 and 0.12, and there are infinite decimals between 0.1111111 and 0.1111112, and (etc.) does that mean that there are infinitely infinite infinitely infinite infinitely infinite infinitely infinite infinitely… (etc.) infinities? — an-salad
As @180 Proof said, set theory goes like that. And since you gave in the example of just rational numbers (0,1111111 and 0,1111112,..) then this is equivalent to the infinity of natural numbers, a countable infinity. With real numbers we get into the more interesting questions.Georg Cantor thought so ... — 180 Proof
That's actually a philosophical view in mathematics. And thus quite well fits a Philosophy Forum.You can build any sort of mathematics (if you wanna call it that) depending on what axioms you choose, the matter is whether it is useful to do and whether it matches at least something in reality. — Lionino
That's actually a philosophical view in mathematics. — ssu
with an axiom of 0=1.
I think you got it a bit wrong. Those who are obsessed about truth or falsity are mathematicians. Even if they sometimes have different axiomatic systems, then it's about right or wrong in that formal system.In Philosophy, they tend to analyse concepts and propositions for truth or falsity. That's what they do. End of the story.
But maybe the mathematicians and scientists do things differently — Corvus
I think you got it wrong too. Philosophers don't care about the truths and falsity as the answers in the answer sheets. Philosophers are more concerned with the truth and falsity in the concepts, propositions, and logic.I think you got it a bit wrong. Those who are obsessed about truth or falsity are mathematicians. Even if they sometimes have different axiomatic systems, then it's about right or wrong in that formal system. — ssu
Yes, Philosophy used to be the parents of all sciences and mathematics. It is the mother of all subjects, and we cannot deny the fact.It's the Philosophers who are interested about a lot more. Things like morals or aesthetics, which obviously aren't about truth or falsity. — ssu
Math and Science pursues the answers in the answer book. You are either right or wrong. Philosophy is more into your arguments and logic for the answers, hence there is no such thing as the answers in the answer book i.e. truth and falsity they pursue are different in nature.? :yikes:
I don't get your point here. — ssu
What answer book?Math and Science pursues the answers in the answer book. — Corvus
Sure, not denying that at all. They are all parts of each other we could say that. They are all inter-related too. But the methodologies they employ and the ideas of their goals might be different depending on the folks who are doing them.What answer book?
I think mathematics is especially interested in logic. I would dare to say that math is part of logic. — ssu
Never said math is not part of philosophy. That is what you are saying for some reason.Just look at ↪Lionino wrote above. Now I don't know if he is a mathematician, but at least he totally understands that philosophy is part of mathematics. — ssu
Have you not read a single math book? If you read any math book, it will have Exercises and Examples after or in the middle of a chapter. The answers for the Exercises will be either at the back of the book, or as a separate Answer Book that you must acquire, if you needed it.Math and Science pursues the answers in the answer book.
— Corvus
What answer book? — ssu
Now I don't know if he is a mathematician, but at least he totally understands that philosophy is part of mathematics. — ssu
We can then say that am,n=m10n+⌊log10(m)⌋��,�=�0�+⌊log10(�)⌋? — Michael
Umm... that's a school math book. Have you even studied a math course in the University? They are a bit different.Have you not read a single math book? If you read any math book, it will have Exercises and Examples after or in the middle of a chapter. The answers for the Exercises will be either at the back of the book, or as a separate Answer Book that you must acquire, if you needed it. — Corvus
I have a few university Calculus and Algebra and Trigonometry books lying around here, and they are full of questions and answers. Studying math means you read the definitions in the books and work on the questions for the answers purely using your reasonings.Umm... that's a school math book. Have you even studied a math course in the University? They are a bit different. — ssu
No. That is not the case. If you study philosophy for the degree, you must read, and write dissertations which you must defend it at a 'viva voce'.And if you study philosophy, you will similarly (hopefully) be given a exam where you have to answer too. — ssu
Norman Wildberger, whose project is to build mathematics without mention of infinity — within the doctrine of finitism — Lionino
Therefore, there can be infinite infinities because the word "infinity" is an adjective. — RussellA
Where can one see the project? — TonesInDeepFreeze
I’m wondering what a thread on mathematics is doing on a philosophy forum. — Joshs
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