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Let me use an example.

y^2 = -x (where y^2 means y squared)

Then y = sq rt (-x). There is an infinite number of solutions, some of which are imaginary numbers and some are real.

So when you say 'infinitely many solutions' this includes imaginary numbers. All real numbers is a subset of that.

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8y ago
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8y ago

A subset of real numbers can also be an infinite set - without including all real numbers. For example:* All integers

* All rational numbers (fractions)

* All multiples of pi (pi multiplied by an integer)

* All numbers of the type 1/n, for an integer n

* Etc.

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8y ago

The set of even integers is a set of infinitely many members but is is not the set of all real numbers.

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Q: What is the difference between infinitely many solutions and all real numbers?
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