n-Dimensional Space

==2024-11-18

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Theory

n-Dimensional Space or n-space is a big challenge for Science. We see the world around us in three dimensions but we encounter many different factors in the world. Every factor is a Dimension to this reality.

Set for n-space

n-space is the set of all possible ordered n-Tuples taken from ${\mathbb{R}}^n$ and is written as:

$V_n={\mathbb{R}}^n=\{\begin{array}{l}\bar{x}:\bar{x}=(x_1,x_2,x_3,\dots ,x_n)\text{ where }{x}_i\in \mathbb{R},1\le i\le n\end{array}$

Here, we have defined the Set for the Vector Space Structures or Systems.

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Important

There aren’t any tuples inside of tuple because they are ordered and we have used the associative property of set multiplication.

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Implementation

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Q&A

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PTR