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EspritFort t1_j69q1e8 wrote

>I get that squaring a negative leads to a solution that’s impossible, but why do you have to make an impossible number into a number? Can’t you just say, “no solution is possible”?

I'm not sure what you mean by "impossible". Could you elaborate on your premise?

Subtracting a number from a smaller number is impossible within the realm of N (Natural Numbers). So why do we need Integers if they are "impossible"?
Well, sometimes we need to subtract a number from a smaller number.

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Tharsis101 OP t1_j69rrqw wrote

I meant square rooted not squared

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macedonianmoper t1_j6b7etg wrote

He understood, the thing is that the square root of a negative number is only impossible if you exclude "imaginary" numbers as a solution.

Very much like saying 3-6 is impossible if you don't think negative numbers are possible.

Just like banks might need negative numbers to say you're in debt, imaginary numbers are useful for other things, engineers use it to describe electricity in AC circuits for example

So you can say that imaginary numbers aren't possible, but that excludes real solutions that help you solve problems, very much like excluding fractional numbers would stop you from sharing an apple with a friend since you can either have an entire apple or none at all

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Ogg8474 t1_j6bjyhu wrote

TIL that N stands for natural numbers.

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Ellykos t1_j6bvvnz wrote

If you didn't know, Z, Q and R are also used. Z are for the integers (-inf to +inf) while N are the natural numbers (0 to +inf). Q is for the rationnal numbers, all the numbers that can be written as a quotient a/b where b isn't equal to 0 (you also have Q' for the irrationnals like pi). Finally R are for the reals. It's important to note that each categorie can contain some of the other categories. For example, all natural numbers are integers, and all integers are real.

EDIT : As commented below, apparently 0 isn't included in N, but in N* (Natural numbers including 0) or W (Whole numbers). Didn't learn it that way, but maybe some people did ?

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The_camperdave t1_j6c57zf wrote

> while N are the natural numbers (0 to +inf)

I was taught that Natural numbers were 1,2,3,..., and Whole numbers were 0,1,2,3...

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Ellykos t1_j6c6rvv wrote

Looking online I can see that W is used for the Whole numbers, but I never saw the W symbol used in all my math classes.

Personally I learned that 0 was a natural number and looking online it is said that 0 was not included in the original definition, but was later added. To avoid mistake, N* is often used to indicate that it contains 0. At the end, it's not really that important but it's good to know !

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[deleted] t1_j6c0vsv wrote

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Ellykos t1_j6c17rj wrote

> integrating by parts

I guess it's a calculus class ? Good luck with that, it was dreadful for me; I had to do the class 3 times before passing the class lol

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[deleted] t1_j6c1e9z wrote

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Ellykos t1_j6c1nvg wrote

Tbf I started really understanding calculus once I was in Uni; I'm now studying engineering and I can integrate in my sleep lol

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