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Determine if this space is complete

Let $T_r = {(x_1,...,x_n) \in \mathbb{R}^n: \sum_{i=1}^n x_i = r}$ and $T_\infty = {(x_1,...,x_n) \in \mathbb{R}^n: x_i \in \mathbb{R} \ \forall i}$. Find the dimension of $T_r$ and $T_\infty$ The answer I have is $T_\infty = \mathbb{R}^n$ and $T_r$ has dimension $r-1$ I have to solve it by finding a subset of $T_\infty$ that is dense and show that this subset is uncountable. What I tried is, $T_\infty$ is complete and $T_r$ is a closed and bounded subset, so $T_r$ is complete. How would I show that this set is dense?

The set is dense. Let ${(x_n}_n\subset T_r$ and $x\in T_\infty$. Then $x_n\to x$ as $ 7582aa13b2 Novicorp WinToFlash Professional 1.5.0000 Portable Â· com.novicorp.wintoflash-professional-1.5.0000-portable.iso-image.. Windows NTÂ . WinToFlash Professional 1.5.0000. Portable file was downloaded to your desktop as: C:\Users\Ajit_\Desktop\WinToFlash Professional 1.5.0000.. Novicorp WinToFlash Professional 1.5.0000 Portable. Developer's Reference. Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â https://documenter.getpostman.com/view/21888973/UzkavYSs https://documenter.getpostman.com/view/21888968/UzkavYSu https://documenter.getpostman.com/view/21908779/UzkavYSv https://documenter.getpostman.com/view/21827461/UzkavYNb https://documenter.getpostman.com/view/21852814/UzkavYSt # Introduction What does your API do?

Overview

Things that the developers should know about

Authentication

What is the preferred way of using the API?

Error Codes

What errors and status codes can a user expect?

Rate limit

Is there a limit to the number of requests a user can send?