- #126

Hans de Vries

Science Advisor

Gold Member

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[itex]\mathbb{R}^n[/itex] is always meant to indicate the standardn-dimensional vector space overR

[itex]\mathbb{R}^n[/itex] is a continues n dimensional vector space. Yes, of course, this is the definition I was using all along.

Which contains an example indicating [itex]\mathbb{R}^3 \otimes \mathbb{R}^3 \cong \mathbb{R}^9[/itex] --I'm using the vector direct product as defined here: http://mathworld.wolfram.com/VectorDirectProduct.htmlnot[itex]\mathbb{R}^6[/itex] as you suggest.

But here you use a 2nd, different definition of [itex]\mathbb{R}^n[/itex]. In this case [itex]\mathbb{R}^n[/itex] means n real elements. OK....

[itex]\mathbb{R}^n[/itex] cannot be denoting a number in this context.

Now [itex]\mathbb{R}^n[/itex] can not denote n real indices or n real elements anymore? As in your 2nd definition?

you insist upon confusing an index set with a vector space 'over' those indices

Are you now accusing me of confusing between the two different interpretations of [itex]\mathbb{R}^n[/itex] you gave ???

You do realize thatR,R²,R³, ... all have the same number of elements, right?

No, define your

**R**,

**R**²,

**R**³ and "elements" properly instead of making a guessing game out of this.

Regards, Hans.

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