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- logic - Difference between $\implies$ and $\;\therefore . . .
Sometimes a single right arrow is used, which has the same meaning It is very common to use the \implies symbol instead of "therefore", but since "implies" and "therefore" have significantly different meanings, this is very bad writing
- What does imply mean in maths? - Mathematics Stack Exchange
Are you asking about the logical symbol $\implies$ ("implies"), or are you asking about how the word "imply" is used in mathematical plain text, e g in proofs The answers to this question seem to be not sure about this
- logic - Difference between $\Rightarrow$ and $\implies$ - Mathematics . . .
I've used both $\\Rightarrow$ and $\\implies$ interchangeably throughout my mathematics in school, and I want to know which is proper When should I use $\\Rightarrow$ over the implies arrow? Does it
- Is $\\curvearrowright$ a valid symbol for implies that?
Implication is almost universally symbolised as $\implies,$ while as you pointed out, material implication doesn't seem to have a universally-agreed on symbol (I prefer $\rightarrow$)
- Understanding the p implies q statement - Mathematics Stack Exchange
0 $ p\implies q $ can be seen as an argument $ p \therefore q$ If the argument is valid and $ p $ is true, then we are sure that $ q $ is also true If the argument is valid and $ p $ is false, we can say nothing about $ q $ using material implication means that we can replace $ p\implies q $ by $ \lnot p \vee q$
- Implication: F $\\implies$ T - Mathematics Stack Exchange
Why is F $\\implies$ T taken as true? Why is this the "convention"?
- Is “implies” the best symbol when rewriting equations?
For a simpler example: " $0 = 1 \implies 1 = 1$ " is true, but " $0 = 1 \therefore 1 = 1$ " is false (Technically $\therefore$ is just logical conjunction, but with an implied hint that the right conjunct is easily derivable from the left conjunct )
- notation - When to use implies - Mathematics Stack Exchange
1 I have made the mistake of using $\implies$ instead of the biconditional in the past Essentially, if you are trying to show equivalences, then it is a good idea to use the biconditional Otherwise, users may become confused, because they will interpret it as meaning that the former implies the latter, but not the other way around
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