- #1
CGandC
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- TL;DR Summary
- .
Suppose I have the following ( arbitrary ) statement:
$$ \forall x\in{S} \ ( P(x) ) $$
Which means: For all x that belongs to S such that P(x).
Can I write it as the following so that they are equivalent? ( although it is not conventional ):
$$ \forall x\in{S} \land ( P(x) ) $$
Can I write this way? what does this mean? ( in plain english it is ambiguous : All x that belongs to S and also P(x) )My reasoning is as follows:
$$ \forall x\in{S} \\ $$ is a statement so I denote it as Q ( not Q(x) since x is a bound variable in this statement ) .
So if i'll look back at the initial statement, i'll write it as follows: $$ Q , ( P(x) ) $$ which I write as $$ Q \land ( P(x) ) $$
Thanks for any help in advance.
$$ \forall x\in{S} \ ( P(x) ) $$
Which means: For all x that belongs to S such that P(x).
Can I write it as the following so that they are equivalent? ( although it is not conventional ):
$$ \forall x\in{S} \land ( P(x) ) $$
Can I write this way? what does this mean? ( in plain english it is ambiguous : All x that belongs to S and also P(x) )My reasoning is as follows:
$$ \forall x\in{S} \\ $$ is a statement so I denote it as Q ( not Q(x) since x is a bound variable in this statement ) .
So if i'll look back at the initial statement, i'll write it as follows: $$ Q , ( P(x) ) $$ which I write as $$ Q \land ( P(x) ) $$
Thanks for any help in advance.