# Do Complex Numbers Exist?

#### inertia

##### Super Member
i.e. sqrt (-1)

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Generally speaking: Is mathematics discovered or is it invented?

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They exist as much as negative numbers do, IMO - you can't have i apples, certainly, but you can't have minus-3 apples, either.

They exist as much as negative numbers do, IMO - you can't have i apples, certainly, but you can't have minus-3 apples, either.

Okay*.

Sabine Hossenfelder is very smart and her viewpoints are strongly within the reductionist / physicalist's camp in the physics community. This strongly-held belief here is that "we gain deeper insights into nature by looking at shorter and shorter distances", and she defends this belief rigorously at times. I also have reason to believe - physicalist - in the sense that she defends her perspective such that physics models nearly all of reality.

That said; how can anyone perform an experiment using a laboratory probe and demonstrate a physical property of sqrt(-1)?

I belief mathematics is a mind tool, an invention if you will - instead of a discovery. ( I have flip-flopped on this idea a number of times though. )

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* One can produce a stipulative definition using ten apples as an initial condition and adding (-3) apples to get seven apples though.

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I think there are real world maths that uses complex numbers, though it could be argued that is a model (but then, is counting apples modelling). I can only vaguely remember one example, which was about electricity and voltage and current were together as a complex number.

I think there are real world maths that uses complex numbers, though it could be argued that is a model (but then, is counting apples modelling). I can only vaguely remember one example, which was about electricity and voltage and current were together as a complex number.

Yes, EE's also designate the imaginary number with a " j " instead of an " i ". Their reasoning is that the letter " i " is also used to model current.

* sqrt(-1) is not an integer
* It is certainly not a rational number
* It's not an irrational number either
* It's not a transcendental number like sqrt (2)
* clocks do not have sqrt(-1) - they only use rational numbers (relativity - imaginary time (Minkowski))

It's as real as the number zero or the number one, and Euler liked it too.

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