I read about Infinitesimal Differential Geometry in this source, page 238-239 and I considered one example while I was reading. I was confused because in this example we have contradiction with definition of product of two sequences.
Example:
Let A is real number.
$A=[t]$
$t=sin(t)+o(t)$ $t$->$0$
$A \approx 0$
If $A \approx 0$ then $A^2 \approx 0$ but it's not true because in accordance with definition of product of two sequences we have:
$t^2=0+o(t)$ $t$->$0$
$A^2=[t]*[t]=[t*t]=0$
So, we get the contradiction.
How is contradiction with definition of product of two sequences possible?