## Adding zero, multiplying times one… are they mathematical operations?

I saw a mathematician explain how the number 1 is not considered a prime number despite it fitting the traditional definition for a prime number; it is a natural number that can be divided by 1 and by itself yielding a natural number as a result. The explanation apparently lied on the Fundamental Theorem of … Read more

## Is this the basic loophole in Zeno’s paradox?

So, Zeno assumes that, to go from the mark at 1m to the mark at 2m we’ve to do an infinite number of tasks. Like the task of getting to 1.001m, the task of getting to 1.000005m,the task of getting to 1.658m,etc. So, to perform an infinite number of tasks, one must take an infinite … Read more

## Truth and undecidability

I believe this is more of a philosophical question. Given a consistent theory T and a statement S independent of T. Can S be true or false in T? (I don’t see any contradiction with that) I read that Godel thinks the Continuum Hypothesis is false (in ZFC ?) even though independent of ZFC. (so … Read more

## Just a thought… defining “competition”?

Let’s think about galaxies and animals. At first, they seem completely different. But their behavior seems to be governed by (or at least arise from) the same rules. Think about competition. Animals and galaxies can be argued to both compete in very life-like ways… Image we have a chemist who makes a new kind of … Read more

## Is $” \sum_{n = 1}^{\infty} (-1)^n \; \text{is a real number}”$ an invalid statement or a false proposition?

So we’re beginning an introductory logic course and my professor is giving examples for valid statements/ propositions – meaningful statements that are either true or false but not both. So he puts forth this one; $$” \sum_{n = 1}^{\infty} (-1)^n \; \text{is a real number}”$$ I said it was a false proposition. My argument was … Read more

## Do all mathematical and logical axiomatic systems implicitly ground natural numbers?

Maybe this question is more suitable for Philsophy SE, but I want to hear mathematicians’ opinions. Suppose that we have an axiomatic system A with axioms A1,A2,A3,…,An,… Notice that this at least implicitly grounds natural numbers, as n∈N is the only reasonable option. (Or is it? I’d love a counterexample to that, if anyone was … Read more

## Is there any theorem that can only be proven using the axiom of choice and that is actually used in real-world applications?

I don’t have a strong background in mathematics but I am interested in it from a philosophical perspective and I was wondering: is there any theorem or mathematical tool that is used in real-world applications and that can only be proven or justified by assuming the axiom of choice to be true? Answer That depends … Read more

## Does Mathematics exists apart from the mathematician? [closed]

Closed. This question is opinion-based. It is not currently accepting answers. Want to improve this question? Update the question so it can be answered with facts and citations by editing this post. Closed 7 years ago. Improve this question Does Mathematics exists apart from the mathematician? Explain yourself. Mathematics seems to be a projection of … Read more

## Error in Introduction to Mathematical Philosophy

Is this an error in the text or am I reading incorrectly. What am I missing? Introduction to Mathematical Philosophy Page 18 Definition of Number “A relation is said to be “one-one” when, if $x$ has the relation in question to $y$, no other term $x_0$ has the same relation to $y$, and $x$ does … Read more

## Are Mathematicians Pluralists About Math?

This has been rangling around my head for awhile. With the death of Hilbert’s program via Gödel’s Incompleteness Theorems (and the prior damage done to Logicism via Russell’s Paradox), have mathematicians become pluralists, of some sort, about their discipline? In ‘Varieties of Logic’, Stewart Shapiro says, “Pluralism about a given subject, such as truth, logic, … Read more