I am unsure if this is the appropriate forum for my question, but I have been struggling to articulate it accurately while searching for a solution online. I am uncertain if I am overthinking the problem or approaching it incorrectly. I will do my best to explain the issue comprehensively.
To provide some context, I have been studying the Levenshtein distance $lev(a,b)$ and I came up with this formulated following equation:
$$p=\left(1-\frac{lev(a,b)}{m}\right)\times100$$
Above equation is used to represent the distance as a percentage in string matching, where $m$ is the length of the longest of the two words. The result is expressed as a percentage.
As part of my "String metric" presentation, I have substituted the equation with example strings. For instance, I have written $p = 80$%.
I am intrigued by the question of whether it is considered appropriate to use the equal sign when representing the decimal form of a percentage, even after multiplying by 100? Specifically, I am wondering if it is valid to express $p=80=0.8$ or simply $p=0.8$. This seems counterintuitive to me since $80$ is not equal to $0.8$ obvious, but it appears to be acceptable when dealing with percentages according to Wikipedia. Wikipedia also employs the equal sign in similar contexts, such as for $0.20 = \frac{20}{100} = 20$%.
Hence, even if I multiply by 100, would $0.8$ or even $\frac{80}{100}$ still be correct?
Alternatively, I have thought of using the implication symbol $\implies$ to represent this scenario. I am uncertain whether it would be appropriate to use it in this context. For instance, would it be acceptable to write $p=80\implies0.8$ instead of $p=80=0.8$.
I appreciate any guidance or clarification you can provide. I apologize if this is not the appropriate forum for my question or if I am approaching it incorrectly. Thank you in advance for your assistance.
Best Answer
When representing percentages, it is common to use the equal sign (=) to indicate equivalence between the percentage value and its decimal form. $80\%$ can be represented as $0.8$. This is because percentages are simply a way of expressing a proportion or ratio out of 100. So, saying "$p = 80\%$" is equivalent to saying "$p = 0.8$". Both statements convey the same information.
The implication symbol ($\implies$) is used to indicates a logical implication or deduction. It denotes that one statement logically implies another.
In the case of representing percentages, the implication symbol is not commonly used because there is no logical implication between the percentage value and its decimal form. It might even cause confusion. Instead, the equal sign ($=$) is used to show the equivalence.
To conclude, it is generally acceptable to use the equal sign ($=$) to represent the equivalence between a percentage value and its decimal form. So, you can write "$p = 80\% = 0.8$". Using the implication symbol ($\implies$) would not be appropriate in this context.