Questions tagged [philosophy]
Questions involving philosophy of mathematics. Please consider if Philosophy Stack Exchange is a better site to post your question.
1,101
questions
1
vote
1
answer
51
views
Zero-dimensional space with multiple objects
I am unsure if this belongs to math or philosophy.
Let's say there's 0-dimensional space, however multiple objects exist within in, occupying the same "spot". If multiple objects exist, is ...
- 115
1
vote
1
answer
125
views
What exactly makes the ordinals an indefinitely extensible concept?
I understand the principles of generation that cantor used to create the ordinals but I cannot see what exactly is the property that makes the ordinals an indefinitely open plurality and not the ...
- 21
0
votes
0
answers
97
views
What did Richard Dedekind mean exactly by his statement about generality?
But—and in this mathematics is distinguished from other sciences—these
extensions of definitions no longer allow scope for arbitrariness; on
the contrary, they follow with compelling necessity from ...
- 27
1
vote
1
answer
99
views
why learning math in elementary school was harder for me rather than upper grades? [closed]
When I was an elementary student, I'd suffered from understanding basic things like multiplication table and other simple things and I had to memorized them. Last hours I was searching for genesis of ...
- 33
1
vote
0
answers
178
views
When mathematicians say "true" do they mean "true in all models"?
According to the comments to this question,
Truth is ordinarily defined by reference to models.
If so, even axioms and theorems are not true without reference to a model.
However, when ...
- 103
0
votes
0
answers
64
views
Arithmetization of Turing machines
Refer to Turing's 1936 paper, page 248, last paragraph. I present the paragraph in verbatim below :
The expression "there is a general process for determining..." has been used throughout ...
- 345
0
votes
0
answers
78
views
Benefits/uses of non-base 10 number systems?
For reference, I'm studying math and anthropology at university, and I've been dying to find some overlap of math theory and ethnomathematics (math uses/tools/systems/etc in other cultures). I'm ...
6
votes
2
answers
887
views
Formally how do we view finite sets
This might be silly, but I have been thinking about how we would work with finite sets very formally.
So, $\{1,2,3,\cdots,n\} = \{k \in \mathbb{Z}^+ \mid k \leq n\}$ gives a representee for which any ...
3
votes
2
answers
273
views
What are fun mathematical facts for non-mathematicians? [duplicate]
I like to spend my life with mathematics. I think it is the best thing I can do in my life. However, I have great difficulty explaining what I am doing to non-mathematicians, even educated ones. For ...
- 375
2
votes
1
answer
100
views
Why is it important to prove that some particular set is a vector space as opposed to just asserting such objects exist?
In Axler's Linear Algebra Done Right Example 1.24, we are asked to prove that the set of all functions from some set S to the set of real (or complex) numbers is a vector space.
I proved this by using ...
user1281086
1
vote
1
answer
69
views
How to get LNC as a theorem using Frege's Prop Calculus?
So Im using axioms from,Frege propositional calculus and is there any way to derive Law of non contradiction as theorem from them.
The axioms
A → (B → A) | THEN-1
(A → (B → C)) → ((A → B) → (A → C)) ...
- 11
-1
votes
1
answer
168
views
What are the differences between equality, equations and identities? [duplicate]
What are the differences between the followings:
Identity
$$
\sin^2(\alpha) + \cos^2(\alpha) = 1
$$
Equation
$$ 4x = 16 $$
Equality - $x,y$ are mathematical objects.
$$ x = y $$
All of the three ...
- 375
-1
votes
2
answers
120
views
Is there a mathematical or physical, real world use for numbers passed I? Who determines what can be conceptualized or not? [closed]
I is the Square root of -1, such that I * I = -1. Through this, I can be considered like a "Half Negative."
Why hasn't this been taken further? Why don't we make a quantity such that I^...
- 37
0
votes
1
answer
287
views
Set theory and model theory: which set is ZFC?
I have yet another post about what is model theory doing and why is it valid; I hope I can be coherent.
(1) https://mathoverflow.net/questions/23060/set-theory-and-model-theory
(2) What exactly is the ...
- 19
13
votes
2
answers
629
views
Probability - Interview Question - Hidden Assumptions and Phrasing Issues
I’ve encountered the following seemingly simple probability interview question in my workplace:
Two reviewers were tasked with finding errors in a book. The first had found 40 errors and the other ...
- 133