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Results tagged with philosophy-of-mathematics
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user 1259
Philosophy of mathematics asks questions about mathematical theories and practices. It can include questions about the nature or reality of numbers, the ground and limits of formal systems and the nature of the different mathematical disciplines.
17
votes
What is the difference between the complex numbers i and -i?
I would probably say that there is really no essential difference between the number i, considered in isolation, and the number -i, considered in isolation. If somebody hands us a system, and we exami …
- 1,498
0
votes
Is mathematics founded on beliefs and assumptions?
We usually think of mathematics as being founded on "axioms". You prove something by starting with axioms (or with theorems that other people have already proven) and using valid logic to derive whate …
5
votes
Why do we equate a mathematical object with what denotes it?
Generally speaking, we don't equate a mathematical object with what denotes it. The symbol A is one thing, and any object that may be denoted by A is a different thing.
Let's consider an analogous sit …
- 1,498
12
votes
If math is so deductive, why is it so hard to discover new math?
I think the premise of the question is false. Actually, it's easy to discover new math.
Here's one way to find some new math. Take a sheet of paper and write down a bunch of "nonsense" equations with …
- 1,498
0
votes
Can the continuum hypothesis be settled in physics?
The continuum hypothesis is already settled. The answer to it is that there are models of set theory in which the continuum hypothesis is true, and there are also models of set theory in which the con …
- 1,498
37
votes
Is infinity a number?
It depends entirely on what you mean by "number." You might be surprised to learn that there is no standard definition of the word "number" in mathematics! Instead, there are many, many different numb …
- 1,498
5
votes
Does science require the exclusion of the "infinite"?
No, there's no need whatsoever to exclude the infinite from science.
The gold standard for a scientific hypothesis is that the hypothesis
is consistent with all known observations,
successfully predi …
- 1,498
4
votes
Can a totally ordered set with a last element but no first element exist, or is this contrad...
Your friend's reasoning doesn't hold up.
The argument that your friend is making is the following. Suppose that a totally ordered set with a last element, but no first element, exists. Then:
Each ele …
- 1,498