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/sci/ - Science & Math

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6504708 No.6504708[DELETED]  [Reply] [Original]

Serious question here /sci/.
Why do people use iff for conditional statements?
Doesn't the word if imply that the following is conditional, which is exactly the thought if and only if conveys?

>> No.6504735

No. If means -->, and iff means <-->. The first just implies that a condition will bring about or indicate something, while the second implies that tis something can *only* be brought about by a certain condition. The two way arrow is important because this also implies that if the something has happened then you can be certain that the condition has been met, whereas if the logical sentence was built with if (-->) the something happening does not imply that any particular condition has been met.

>> No.6504757

>>6504708
"A if B" means that B implies A.
"A only if B" means that A implies B.
"A if and only if B" means that A and B imply each other.

>> No.6504764

>>6504757
in arrows thats
only if <span class="math">\Longrightarrow [/spoiler]
needs (if) <span class="math"> \Longleftarrow [/spoiler]
if and only if <span class="math"> \iff [/spoiler]
yeah?

>> No.6504770

>>6504764
yup, that's correct. Does this help, OP?

>> No.6504902

Different person here
I'm fairly certain that in the English language, if is intended to refer to iff, so why was iff invented?

>> No.6504912

>>6504902
It's totally ambiguous and context-dependent in the english language.

>If I ever feel frustrated, I'll just go for a walk to calm down

Would you expect this person never to leave their house unless frustrated?

So in math and logic, we treat if to have one meaning and make a new word iff to take on the other meaning.

It's the same with OR and XOR.

>> No.6504915

>>6504902
It doesn't, in some instances maybe it's meant to be interpreted that way but in formal logic there is a difference and it needs to be made exactly clear which statement you're making.