I'm having trouble visualizing this geometrically - why is it that multiplying the U,V coordinates of a texture coordinate has the effect of scaling that texture by that factor?

eg if you scaled the texture coordinates by a factor of 3 ..then doesn't this mean that if you had texture coordinates 0,1 and 0,2 ...you'd be sampling 0,3 and 0,6 in the U,V texture space of 0..1? How does that make it bigger

eg HLSL: tex2D(textureSampler, TexCoords*3)

Integers make it smaller, decimals make it bigger

I mean I understand intuitively if you added to the U,V coordinates, as that is simply an offset into the sampling range, but what's the case with multiplication?

I have a feeling when someone explains this to me I'm going to be feeling mighty stupid