Does minus infinity^2 equal infinity?

Does minus infinity^2 equal infinity?
Or if not, what exactly is the result?

[Image removed]

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JanyoOoO
10 months ago

No potencies are defined for infinity (no matter if plus or minus).

But once thought, you would treat infinity like a number x. Then it depends on how to treat the expression.

  1. -×^2 = -(x^2) would be the standard case. The potency finally prevails. In this case, it would still be negative.
  2. -x^2=(-x)^2 would actually be a wrong forming. The case corresponds to y^2=(y)^2 for y=-x. In this case, it would actually be Plus Infinite.

So it depends on where the minus is and whether there are brackets.

verreisterNutzer
10 months ago
Reply to  JanyoOoO

Great, thanks! I added another picture to my question. So after your explanation, it would always be infinite, as the minus is in the clamp with the infinity.

JanyoOoO
10 months ago

That’s all right. You don’t expect to be infinity, but do a general transformation of (-x)^2 to x^2. This is generally clear. Then x can assume any desired value. It is also beneficial that x is not the same infinity, but goes against infinity. That makes a formal difference.

Halbrecht
10 months ago

So can I always accept that?

No. If you introduce a very small (- 10000 is smaller than -100 ) number instead of (- inend)2, then this is fine.

The teacher has already capitulated before the declining cognitive capacity among the pupils that she writes so mathematically false. Because with infinity you cannot deal with a number

.

By the way, the whole can be solved much faster with x^5/x^3 = x^2

Tannibi
10 months ago

Nothing. Infinity is not a number, so you can
not counting. Infinitely minus Infinite is e.g. not zero.

evtldocha
10 months ago

If the spelling comes from your mathematician teacher on the solution sheet in addition to the question, this is rather bitter.

ChrisGE1267
10 months ago
Reply to  evtldocha

This seems to me to be the educational standard of the present…