# I Can the area be understood as the "number of points"?

#### WWGD

Gold Member
The only model of this I can think of is that of n-squares, a line broken into dx_i ,lengths a volume broken into cubes $dxdyf(x_k,y_k)$ assuming converfence,,etc. Volume is the number of such units/scaled cubes. Edit I remember a contest a while back on counting the number of gumballs in a jar. This was , essentially the volume in gumball units instead of cc.

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#### WWGD

Gold Member
A problem is that both, e.g., a square of side 1, side 2, any finite size will have areas $1,4,.., n^2$ respectively but each will have uncountably-many points, so measure and cardinality are different concepts.

#### meopemuk

I recommend you to look into the field called "nonstandard analysis." They invented clever ways to think about infinities. Perhaps you can even define "the number of points in a line" using their methods? Not sure.

Eugene.

"Can the area be understood as the "number of points"?"

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