Btukfyl

Using the following packages;

documentclass{article}

usepackage[utf8]{inputenc}

usepackage[english]{babel}

usepackage{fancyhdr}

usepackage{amsthm}     

usepackage{float}

usepackage[round]{natbib}

usepackage{lastpage}

usepackage{indentfirst}

usepackage{graphicx}

usepackage{amsmath}

It says undefined control sequence when writing

{It is called a simple arc of a curve, the set $C$ of points $M(x,y) in text{$R$} ^2 $ 

(two-dimensional Euclidean space) satisfying the equation:} 

also changing this to the following doesn't work

{It is called a simple arc of a curve, the set $C$ of points $M(x,y) in R ^2 $ 

I have included

usepackage{amsmath}

like it says to do to fix the issue on most forums

R is not a standard LaTeX command and is not defined by any of the packages you load. It's a custom command that a lot of people seem to like, but you have to define it yourself. Presumably you want something like

newcommand{R}{mathbb{R}}

Although I myself recommend against it. The reasons are subtle. There's nothing to stop you defining one letter commands like R and, as many discussions on this site have concluded, R is not inherently any more or less dangerous than realnumbers, however a lot of people land themselves in trouble because they don't realise that a lot of one letter commands are already defined by LaTeX. They then define over them and get weird errors that cause a lot more problems than they're worth. R is also pretty syntactically meaningless. Myself, if I had to do this, I would go with reals instead, I think, but this is really none of my business, it's up to you what shortcuts you wish to define, if, indeed, you wish to define them.

Anyway, you will need the amssymb package for this to work, or amsfonts, since they define mathbb{}.

documentclass{article}

usepackage{amsmath}

usepackage{amssymb}



newcommand{R}{mathbb{R}}



begin{document}



It is called a simple arc of a curve, the set $C$ of points

$M(x,y) in R^{2}$



end{document}

In other news, I'm not quite sure why you seem to have braces around your sentence, in general they would not be needed so I've removed them here.

To expand on the excellent accepted answer: There are many alternatives to amsfonta for this symbol.

In the modern toolchain, there is no need to load any additional packages beyond unicode-math to get a ℝ that looks like the one from the early answer. It is already set up by default.

However, you can load the double-struck alphabet from any math font, or any display font that you’d rather use, with the range= option of setmathfont. For example, to use Typoliner:

documentclass[varwidth]{standalone}

usepackage{unicode-math}



defaultfontfeatures{Scale=MatchUppercase}



setmathfont{Latin Modern Math}

setmathfont[range=bb]{Typoliner-RW-Light.ttf}



newcommandsetR{symbb{R}}



begin{document}

Let (S subset setR).

end{document}

If you need compatibility with PDFLaTeX, or you would rather use a legacy NFSS font, you might want to use the mathalfa package to select your supplemental math alphabets.