Revisions to What practical applications does set theory have?

added a Wayback Machine link for the dead link

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edited Aug 5, 2021 at 7:23

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I am a non-mathematician. I'm reading up on set theory. It's fascinating, but I wonder if it's found any 'real-world' applications yet. For instance, in high school when we were learning the properties of i, a lot of the kids wondered what it was used for. The teacher responded that it was used to describe the properties of electricity in circuits. So is there a similar practical app of set theory? Something we wouldn't be able to do or build without set theory?

Edit: Actually, I'm asking about the practicality of the knowledge of the properties of infinite sets, and their cardinality. I'm reading Peter Suber's [A Crash Course in the Mathematics Of Infinite Sets][1] ([Wayback Machine](https://web.archive.org/web/20110703003113/https://earlham.edu/~peters/writing/infapp.htm)). The properties of infinite sets seem unintuitive, but of course, the proofs show that they are true.

My guess is that whoever came up with the square root of -1 did so many years before it 'escaped' from mathematics and found a practical use. Before then perhaps people thought it was clever, but not necessarily useful or even 'true'. So then, if you need to understand electricity, and you can do it best by using i, then even someone who thinks it's silly to have a square root of negative -1 would have to grudgingly admit that there's some 'reality' to it, despite its unintuitiveness, because electricity behaves as if it 'exists'.

Seeing as how there was so much resistance to infinite sets at the beginning, even among mathematicians, I wonder: has the math of infinite sets been 'proven worthwhile' by having a practical application outside of mathematics, so that no one can say it's just some imaginative games?

I am a non-mathematician. I'm reading up on set theory. It's fascinating, but I wonder if it's found any 'real-world' applications yet. For instance, in high school when we were learning the properties of i, a lot of the kids wondered what it was used for. The teacher responded that it was used to describe the properties of electricity in circuits. So is there a similar practical app of set theory? Something we wouldn't be able to do or build without set theory?

Edit: Actually, I'm asking about the practicality of the knowledge of the properties of infinite sets, and their cardinality. I'm reading Peter Suber's [A Crash Course in the Mathematics Of Infinite Sets][1]. The properties of infinite sets seem unintuitive, but of course, the proofs show that they are true.

My guess is that whoever came up with the square root of -1 did so many years before it 'escaped' from mathematics and found a practical use. Before then perhaps people thought it was clever, but not necessarily useful or even 'true'. So then, if you need to understand electricity, and you can do it best by using i, then even someone who thinks it's silly to have a square root of negative -1 would have to grudgingly admit that there's some 'reality' to it, despite its unintuitiveness, because electricity behaves as if it 'exists'.

Seeing as how there was so much resistance to infinite sets at the beginning, even among mathematicians, I wonder: has the math of infinite sets been 'proven worthwhile' by having a practical application outside of mathematics, so that no one can say it's just some imaginative games?

I am a non-mathematician. I'm reading up on set theory. It's fascinating, but I wonder if it's found any 'real-world' applications yet. For instance, in high school when we were learning the properties of i, a lot of the kids wondered what it was used for. The teacher responded that it was used to describe the properties of electricity in circuits. So is there a similar practical app of set theory? Something we wouldn't be able to do or build without set theory?

Edit: Actually, I'm asking about the practicality of the knowledge of the properties of infinite sets, and their cardinality. I'm reading Peter Suber's [A Crash Course in the Mathematics Of Infinite Sets][1] ([Wayback Machine](https://web.archive.org/web/20110703003113/https://earlham.edu/~peters/writing/infapp.htm)). The properties of infinite sets seem unintuitive, but of course, the proofs show that they are true.

My guess is that whoever came up with the square root of -1 did so many years before it 'escaped' from mathematics and found a practical use. Before then perhaps people thought it was clever, but not necessarily useful or even 'true'. So then, if you need to understand electricity, and you can do it best by using i, then even someone who thinks it's silly to have a square root of negative -1 would have to grudgingly admit that there's some 'reality' to it, despite its unintuitiveness, because electricity behaves as if it 'exists'.

Seeing as how there was so much resistance to infinite sets at the beginning, even among mathematicians, I wonder: has the math of infinite sets been 'proven worthwhile' by having a practical application outside of mathematics, so that no one can say it's just some imaginative games?

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edited Mar 9, 2021 at 0:31

Rodrigo de Azevedo

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fixed some grammar

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edited May 8, 2017 at 13:11

Todd Trimble

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I am a non-mathematician. I'm reading up on set theory. It's fascinating, but I wonder if itsit's found any 'real-world' applications yet. For instance, in high school andwhen we were learning the properties of i, a lot of the kids wondered what it was used for. The teacher responded that it was used to describe the properties of electricity in circuits. So is there a similar practical app of set theory? Something we wouldn't be able to do or build without set theory?

Edit: Actually, I'm asking about the practicality of the knowledge of the properties of infinite sets, and their cardinality. I'm reading Peter Suber's [A Crash Course in the Mathematics Of Infinite Sets][1]. The properties of infinite sets seem unintuitive, but of course, the provesproofs show that they are true.

My guess is that whoever came up with the square root of -1 did so many years before it 'escaped' from mathematics and found a practical use. Before then perhaps people thought it was clever, but not necessarily useful or even 'true'. So then, if you need to understand electricity, and you can do it best by using i, then even someone who thinks it's silly to have a square root of negative -1 would have to grudgingly admit that there's some 'reality' to it, despite its unintuitiveness, because electricity behaves as if it 'exists'.

Seeing as how there was so much resistance to infinite sets at the beginning, even among mathematicians, I wonder: has the math of infinite sets bebeen 'proven worthwhile' by having a practical application outside of mathematics, so that no one can say it's just some imaginative games?

I am a non-mathematician. I'm reading up on set theory. It's fascinating, but I wonder if its found any 'real-world' applications yet. For instance, in high school and we were learning the properties of i, a lot of the kids wondered what it was used for. The teacher responded that it was used to describe the properties of electricity in circuits. So is there a similar practical app of set theory? Something we wouldn't be able to do or build without set theory?

Edit: Actually, I'm asking about the practicality of the knowledge of the properties of infinite sets, and their cardinality. I'm reading Peter Suber's [A Crash Course in the Mathematics Of Infinite Sets][1]. The properties of infinite sets seem unintuitive, but of course, the proves show that they are true.

My guess is that whoever came up with the square root of -1 did so many years before it 'escaped' from mathematics and found a practical use. Before then perhaps people thought it was clever, but not necessarily useful or even 'true'. So then, if you need to understand electricity, and you can do it best by using i, then even someone who thinks it's silly to have a square root of negative -1 would have to grudgingly admit that there's some 'reality' to it, despite its unintuitiveness, because electricity behaves as if it 'exists'.

Seeing as how there was so much resistance to infinite sets at the beginning, even among mathematicians, I wonder: has the math of infinite sets be 'proven worthwhile' by having a practical application outside of mathematics, so that no one can say it's just some imaginative games?

I am a non-mathematician. I'm reading up on set theory. It's fascinating, but I wonder if it's found any 'real-world' applications yet. For instance, in high school when we were learning the properties of i, a lot of the kids wondered what it was used for. The teacher responded that it was used to describe the properties of electricity in circuits. So is there a similar practical app of set theory? Something we wouldn't be able to do or build without set theory?

Edit: Actually, I'm asking about the practicality of the knowledge of the properties of infinite sets, and their cardinality. I'm reading Peter Suber's [A Crash Course in the Mathematics Of Infinite Sets][1]. The properties of infinite sets seem unintuitive, but of course, the proofs show that they are true.

My guess is that whoever came up with the square root of -1 did so many years before it 'escaped' from mathematics and found a practical use. Before then perhaps people thought it was clever, but not necessarily useful or even 'true'. So then, if you need to understand electricity, and you can do it best by using i, then even someone who thinks it's silly to have a square root of negative -1 would have to grudgingly admit that there's some 'reality' to it, despite its unintuitiveness, because electricity behaves as if it 'exists'.

Seeing as how there was so much resistance to infinite sets at the beginning, even among mathematicians, I wonder: has the math of infinite sets been 'proven worthwhile' by having a practical application outside of mathematics, so that no one can say it's just some imaginative games?