Approximation Notations

Question

Given $A\approx B$ and $B=C$.

Isn't it incorrect for some textbooks to write them together like $A\approx B=C$ rather than $A\approx B\approx C$?

Because

$A$

$\approx B$

$=C$

is essentially saying $A=C$ if we cut the middle-man, which is false!

Another example:

$1$

$=0.5+0.5$

$=2-1$

$=1$

Cut out the middle derivations and we get $1=1$ which is true.

Answer 1

Given $A≈B$ and $B=C$.

Isn't it incorrect for some textbooks to write them together like $A≈B=C$ rather than $A≈B≈C$?

No, the textbooks are correct.

Note that the combined statement $A≈B=C$ means $A≈B$ and $B=C$ which is what you'd like to claim.

On the other hand $A≈B≈C$ means $A≈B$ and $B≈C$ which is not what you'd like to claim because it does not imply the equality of $B$ and $C$ as it was intended.