I've been trying to figure out what the correct notation for saying that something can be substituted as something else.

Example: $y=Re*4$ where $Re=\frac{uL}{\nu}$

Is there an appropriate symbol to "where"? Note that "when" and "given" can easily replace "where" in this example.

I did see this question, but most of the answers were tackling how to write the even condition rather than how to relate the two objects together. Also in that example, it's really difficult to tell whether their using the "|" as a "divides by" or a "given" according to Wikipedia's list

  • $\begingroup$ $\mid$ means "given" only in the context of probability: it refers to a random variable conditioned on something. $\endgroup$ – Patrick Stevens Oct 1 '17 at 17:50
  • $\begingroup$ Typically, I would just spell it out, as you have done. $\endgroup$ – Xander Henderson Oct 1 '17 at 18:02

The way I think about this is as you said in your example, $y = Re * 4$, where $Re = \frac{uL}{v}$. Here we are saying explicity that $Re$ can be something else.

If we would use "when" instead. The way at least I would use "when" is e.g. $y = 4$, when $Re = 1$. Here we're declaring specific values of $Re$, instead of saying that it always holds true for substitution.

The way I would use "given" is more in the same way that I could use "when".

Each of the three could probably be substituted by each other and people would still understand it and not really think about it; but I would use "where" for abstract substitutions of unknowns. And "when" and "given" for specific values of something that makes something else true within the expressions.


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