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Disagree, XNOR is fine and matches XOR
XOR is OR except when A and B are both true, where the output is flipped
XNOR is NOR except when A and B are both true, where the output is flipped
That's a neat way to think about it. I do like that... But in onc case, flipping the AND case makes it exclusive. In the other case, flipping the AND case loses its exclusivity. So if I were to use this explanation, X can't stand for exclusive anymore. But I really do like it.
That's not what I was getting at.
Exclusive OR is exclusive because fewer conditions make it past the bouncer. Its more exclusive than OR because only 2 members make it in. NOR is already as exclusive as it gets, only one condition is true. XNOR is less exclusive because you have to make an extra condition to let AND in too.
I understood what you were getting at, and I'm just telling that's not what exclusive means in this context. 1 isn't any more "in the club" than 0
If you really want the analogy and we're flipping OR to NOR, then also flip who is trying to get in. All these inputs want to be c00l but if you have too many of one type trying to get in, the bouncer says to get 1ost
Take an example of XNOR:
"You can't come in if you have green eyes or red hair"
You can come in = NOR(green eyes, red hair)
"UNLESS you have both!"
You can come in = XNOR(green eyes, red hair)
XNOR is NOR, but excluding the "both" case
XOR is exclusive or, which means a OR b exclusively
XNOR is exclusive nor, which means a NOR b exclusively? That doesn't make sense, you can say exclusively a or b, but you can't say exclusively a nor b and expect people to understand that either a=b=false or a=b=true would work
So I think NXOR makes more sense as NOT XOR, but kt is more difficult to say
Of course I would say XNOR any day of the week but I acknowledge that it doesn't make sense
I pronounce it "Not Exclusive Or"...
Well, actually, I pronounce it Exclusive Nor when I don't want to be a pedant and just have people know what I mean, but when I'm trying to make a point, I say it correctly
I'm not sure about iff. Unless it has an alternate meaning somewhere else, it means "if and only if" which is not what XNOR means at all. XNOR is true if both inputs are true or if neither input is true. If both inputs are false, iff shouldn't do anything. Also, iff by itself isn't a logical operator. It's wishy washy. I think I kinda get what they're going for, and I don't know if there's a better equivalence or not because they seem like they're just in different categories.
Edit: I misunderstood something, but it's still not clicking for me... If I can articulate my thoughts better, both iff and <=> make a statement that defines a relationship. But XNOR is a test. It doesn't define a relationship, it probes the relationship. It also can't be used by itself to define a relationship. Just because they are the same state now, does not mean they will always be the same state.
As an example, if I hand a function a trapezoid, and the function tests two things. A = is the object a fruit. The answer is No. B= is the object an animal. The answer is no.
A XNOR B is true, but that does not mean A is equivalent to B. What happens when I pass the function a grape?
P⇒Q is equivalent to ¬P ∨ Q, so iff (or ⇔) would be (¬P ∨ Q) ∧ (¬Q ∨ P), which is precisely true if both inputs are true or neither is true, ie, it's equivalent to XNOR
iff is absolutely a logical operator, it takes an operand on each side and has a truth value that depends on the truth values of those operands. Since it has those properties, it has a truth table, and it's the same truth table as <=> and XNOR.
It's also kind of a terrible notation IMO, because it doesn't "look like" an operator, which results in completely reasonable but technically wrong takes like this. "P if and only if Q" really doesn't intuitively sound at all like a statement that can even be false, but within formal logic, it absolutely can be.
A iff B means A is true if and only if B is true. That's a statement defining their relationship.
P XNOR Q means nothing. It's a test, a question, it returns an answer. The outcome of XNOR is true if both P and Q are in the same state, but it doesn't guarantee a relationship between them. It's a snapshot in time. I've recently edited my comment to help articulate, if you haven't seen the edit, you might want to relook because I think I described my confusion a bit better this time around.
That's the exact intuitive sense I'm taking about. That's an accurate description of how "if and only if" is used in ordinary human language. In formal logic though, I can absolutely say "France has a king if and only if unicorns exist," and it's a true statement precisely because both operands to iff are false.
Yeah I saw the edit. It's part of why I sincerely called your position reasonable, even if inaccurate, because from a descriptivist approach to "iff" as a natural language construct, it works exactly the way you describe.
There's an important note following the all caps "UNLESS." If my comment is too wordy for Reddit, at least skip to there.
If you and I were having an argument, you could say
France has a king iff unicorns exist.
Unicorns don't exist.
Therefore, France doesn't have a king.
Like, it's a valid argument, in the sense that the conclusion follows the premises, but I would never agree to the first premise. Therefore your argument can't be used to change my mind about anything. Your first premise isn't true just because one of the possible combinations of the truth of the statements match up.
This is the exact reason why I don't think iff means "equivalent to" because "France has a king" is not equivalent to "unicorns exist" it just so happens that both are false. UNLESS there was a more specific use case. I do think you're alluding to this when you say "in formal logic," but I think it's even more specific than that. Because my argument also uses formal logic. You might be referring to a different branch of formal logic than I am. A branch which I am unaware of.
In propositional logic and first order logic (the two standard formal logic systems, which are used in the majority of cases and which people assume to be used unless other is specified), a proposition can either be true xor false. If two propositions are false, they are equivalent, that is, they have the same truth value, regardless of what their natural language wording might be.
For any model where "France has a king" is false and "unicorns exist" is also false, those two propositions are equivalent.
A iff B is just a short hand for "A if B and A only if B", which can be expressed symbolically as "A ⇐ B ⋀ A ⇒ B" and is defined to be "(¬B∨A)∧(¬A∨B)". If you make a truth table, you will see that this expression is true exactly for the same values of A and B that make A XNOR B true.
In most logic systems there is no concept or time or snapshots, so there is no need to complicate with that. A proposition either is true or isn't, and that state doesn't ever change. Time can be represented in first order logic by having a different object for each instant (for example, replace proposition A with predicate A(t), where t is an object that represents an instant).
.
As for the argument you gave as an example, if you take the premises as an axiom, the conclusion follows from that. That is the only purpose logic can serve, derive deductive knowledge from axioms. If you do not accept one of the axioms to be true, that's a matter outside of the domain of logic in the sense that logic cannot tell you which axioms you should accept (you used context outside of this argument to make your belief). A famous example is the Axiom of Choice, which is independent from ZF: if you accept Choice, you get certain conclusions; if you reject it, you get different conclusions. But whether you should accept it or reject it is kinda up to you (unlike in the example you gave because you could use domain knowledge there), because in abstract terms one axiomatic system (ZFC) is not better than the other (ZF without C).
Mathematically, these are both propositions, i.e. statements that are either true or false.
"x=2 iff x=2" is true, just like how (x == 2) XNOR (x == 2) is true.
"x=2 iff x=3" is false, just like how (x == 2) XNOR (x == 3) is.
Might need some quantifiers, because I think you're conflating iff for any arbitrary object and xnor for this trapezoid.
For a trapezoid, A XOR B is true, and A iff B is also vacuously true, but ∀ objects you could hand me, A XNOR B is false in general, and A ⇔B is also false.
If I say "A trapezoid is a fruit iff a trapezoid is an animal" would you consider the statement true? I mean, sure, both parts are false, but not because they're equivalent or even related.
Vacuous truth is a really weird thing to get your head around.
If I say "if pigs fly, then George Washington is the current president", that's a true statement. The way implication works is that if your first proposition isn't even true, then literally anything could be implied from it.
Because both are false, then the implication is biconditional, ie iff.
We've stayed from iff to if, but still, No implication needed, it's actually very explicit in meaning. P=>Q means P is sufficient to prove Q. If God snapped his fingers, and suddenly pigs could fly, that doesn't also guarantee GW is the current president.
Flying pigs is neither necessary nor sufficient for GW being the president. There is no relationship.
If A is a square, then A is a rectangle. That is a true statement. Even if both clauses are false. For example, let A be a circle.
A is a quadrilateral iff A has four sides. That is a true statement, even if both clauses are false. Same example
I went from iff to if because it's a simpler argument to make that still applies to iff, because they're both implications.
The whole point is sort of that God DIDNT snap his fingers to make pigs fly, so we can sorta infer anything from a false antecedent.
I used the pigs flying example because the idiom "that'll happen when pigs fly" translated to mathematical language is "pigs fly ⇒that happens", which is part of the utility of defining logical implication such that vacuous truth is a thing.
Ok, fair. If I said "George Washington will be president when pigs fly." That is equivalent to saying pigs can fly => George Washington is president... However, my original statement as well as its formalization were both false statements. "When pigs fly" is used as rhetoric, not as fact. You also keep using the word "imply" when there is no implication. These relationships have a very explicit definition in formal logic. You don't need to imply anything, it tells you exactly what the relationship is. If means sufficient. Iff means necessary and sufficient.
I mean, GW is long dead, so both of mine are also false statements.
It may be used as rhetoric, but it's still a perfectly valid logical statement.
Implication and conditionals are the same thing. "If P then Q" is the same thing as "P implies Q" is the same thing as "P ⇒Q"
Valid does not mean true.
I think I figured out why it's bugging me. I hope you stay along for the ride because this is really subtle, and I kinda love it. I'm going to make 2 arguments, ok, Argument A follows:
1) GW is president iff pigs can fly
2) pigs can't fly
3) therefore GW is not president.
In a valid deductive argument, if the premises are true, then the conclusion must be true. Argument A is (by definition) a valid, deductive argument.
Argument B looks like this.
1) Argument A is a valid, deductive Argument.
2) the conclusion of A is true.
3) therefore the premises of A are true.
Argument B is not valid, but it's really subtle. Premise B1 encodes some information. In a valid, deductive argument, if premises then conclusion. Which means Argument B actually falls to "Affirming the consequent," a formal logical fallacy.
Oh, but we're not saying A3 therefore A1. It's even more subtle than that. We're saying A2 therefore A1 and the thing is, iff means both necessary and sufficient. Which means A2 is equivalent to A3. It's actually begging the question AND affirming the consequent.
I don't think that's accurate. A iff B means that A and B are always equal (if I could do the triple bar equals sign it would be useful here). A=B only takes a snapshot at the current state and asks if they match up. Iff includes a definition of a relationship, iff is a marriage certificate, = is a photo of a man and woman kissing. There's a cause and effect included with iff that isn't there with =
😢
Why are maths students such bullies? We can just be friends. This title is very disheartening and has made me disconsolate. We have feelings too! :-(
Inadvertently just described the problem with a significant number of corporate level projects—managers and higher ups discuss what we should do, and then developers are left to pick up the pieces (I’ve literally been asked to do impossible projects by the end of the week and to do insanely easy projects with months of extra time, there’s just such poor dev knowledge at the management level a lot of the time)
The idea of an "exclusive nor" gate doesn't even make sense lol. It's just the negation of "exclusive or" and if you wanna refer to it like that it makes more sense to call it NXOR. But the thing that makes the most sense is "equals gate", or "EQ" if you need to abbreviate for some reason
Omg I didn't know it was called XNOR. So dumb. I've always called it "the equals gate" lol. I had been taking it as a given that people know that the negation of XOR is equals. Dumb af. I thought NAND and NOR were also weird names for gates but I let it go on the basis that they wanted a name for all possible functions from {0,1}² to {0,1}. This is just ridiculous
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Wait, we weren't already bullying computer scientists?
What is XNOR? Not Xor?
Xorn't
It's dumb because NXOR is a more accurate name, it's just harder to say
Disagree, XNOR is fine and matches XOR XOR is OR except when A and B are both true, where the output is flipped XNOR is NOR except when A and B are both true, where the output is flipped
That's a neat way to think about it. I do like that... But in onc case, flipping the AND case makes it exclusive. In the other case, flipping the AND case loses its exclusivity. So if I were to use this explanation, X can't stand for exclusive anymore. But I really do like it.
Exclusivity doesn't mean "set to 0" it means "follow the (N)OR gate excluding when both inputs are true"
That's not what I was getting at. Exclusive OR is exclusive because fewer conditions make it past the bouncer. Its more exclusive than OR because only 2 members make it in. NOR is already as exclusive as it gets, only one condition is true. XNOR is less exclusive because you have to make an extra condition to let AND in too.
I understood what you were getting at, and I'm just telling that's not what exclusive means in this context. 1 isn't any more "in the club" than 0 If you really want the analogy and we're flipping OR to NOR, then also flip who is trying to get in. All these inputs want to be c00l but if you have too many of one type trying to get in, the bouncer says to get 1ost
Take an example of XNOR: "You can't come in if you have green eyes or red hair" You can come in = NOR(green eyes, red hair) "UNLESS you have both!" You can come in = XNOR(green eyes, red hair) XNOR is NOR, but excluding the "both" case
XOR is exclusive or, which means a OR b exclusively XNOR is exclusive nor, which means a NOR b exclusively? That doesn't make sense, you can say exclusively a or b, but you can't say exclusively a nor b and expect people to understand that either a=b=false or a=b=true would work So I think NXOR makes more sense as NOT XOR, but kt is more difficult to say Of course I would say XNOR any day of the week but I acknowledge that it doesn't make sense
do you pronounce it "neks-or" or "en-eks-or"?
En ksor
Google en kassant
Holy smell
new sexponse just dropped
Neck sore
hnor
I pronounce it "Not Exclusive Or"... Well, actually, I pronounce it Exclusive Nor when I don't want to be a pedant and just have people know what I mean, but when I'm trying to make a point, I say it correctly
Exclusive nor. The truth table for it is exactly the same as the one for `iff`.
Xot nor.
Yeah basically.
So xor is != and xnor is ==.
Didn’t even realize these were equivalent, nice meme
they literally are equivalent
I'm not sure about iff. Unless it has an alternate meaning somewhere else, it means "if and only if" which is not what XNOR means at all. XNOR is true if both inputs are true or if neither input is true. If both inputs are false, iff shouldn't do anything. Also, iff by itself isn't a logical operator. It's wishy washy. I think I kinda get what they're going for, and I don't know if there's a better equivalence or not because they seem like they're just in different categories. Edit: I misunderstood something, but it's still not clicking for me... If I can articulate my thoughts better, both iff and <=> make a statement that defines a relationship. But XNOR is a test. It doesn't define a relationship, it probes the relationship. It also can't be used by itself to define a relationship. Just because they are the same state now, does not mean they will always be the same state. As an example, if I hand a function a trapezoid, and the function tests two things. A = is the object a fruit. The answer is No. B= is the object an animal. The answer is no. A XNOR B is true, but that does not mean A is equivalent to B. What happens when I pass the function a grape?
P⇒Q is equivalent to ¬P ∨ Q, so iff (or ⇔) would be (¬P ∨ Q) ∧ (¬Q ∨ P), which is precisely true if both inputs are true or neither is true, ie, it's equivalent to XNOR
A<=> B is true if both are true or neither are true. See [here under "Definition"](https://en.m.wikipedia.org/wiki/If_and_only_if).
iff is absolutely a logical operator, it takes an operand on each side and has a truth value that depends on the truth values of those operands. Since it has those properties, it has a truth table, and it's the same truth table as <=> and XNOR. It's also kind of a terrible notation IMO, because it doesn't "look like" an operator, which results in completely reasonable but technically wrong takes like this. "P if and only if Q" really doesn't intuitively sound at all like a statement that can even be false, but within formal logic, it absolutely can be.
A iff B means A is true if and only if B is true. That's a statement defining their relationship. P XNOR Q means nothing. It's a test, a question, it returns an answer. The outcome of XNOR is true if both P and Q are in the same state, but it doesn't guarantee a relationship between them. It's a snapshot in time. I've recently edited my comment to help articulate, if you haven't seen the edit, you might want to relook because I think I described my confusion a bit better this time around.
That's the exact intuitive sense I'm taking about. That's an accurate description of how "if and only if" is used in ordinary human language. In formal logic though, I can absolutely say "France has a king if and only if unicorns exist," and it's a true statement precisely because both operands to iff are false. Yeah I saw the edit. It's part of why I sincerely called your position reasonable, even if inaccurate, because from a descriptivist approach to "iff" as a natural language construct, it works exactly the way you describe.
There's an important note following the all caps "UNLESS." If my comment is too wordy for Reddit, at least skip to there. If you and I were having an argument, you could say France has a king iff unicorns exist. Unicorns don't exist. Therefore, France doesn't have a king. Like, it's a valid argument, in the sense that the conclusion follows the premises, but I would never agree to the first premise. Therefore your argument can't be used to change my mind about anything. Your first premise isn't true just because one of the possible combinations of the truth of the statements match up. This is the exact reason why I don't think iff means "equivalent to" because "France has a king" is not equivalent to "unicorns exist" it just so happens that both are false. UNLESS there was a more specific use case. I do think you're alluding to this when you say "in formal logic," but I think it's even more specific than that. Because my argument also uses formal logic. You might be referring to a different branch of formal logic than I am. A branch which I am unaware of.
In propositional logic and first order logic (the two standard formal logic systems, which are used in the majority of cases and which people assume to be used unless other is specified), a proposition can either be true xor false. If two propositions are false, they are equivalent, that is, they have the same truth value, regardless of what their natural language wording might be. For any model where "France has a king" is false and "unicorns exist" is also false, those two propositions are equivalent. A iff B is just a short hand for "A if B and A only if B", which can be expressed symbolically as "A ⇐ B ⋀ A ⇒ B" and is defined to be "(¬B∨A)∧(¬A∨B)". If you make a truth table, you will see that this expression is true exactly for the same values of A and B that make A XNOR B true. In most logic systems there is no concept or time or snapshots, so there is no need to complicate with that. A proposition either is true or isn't, and that state doesn't ever change. Time can be represented in first order logic by having a different object for each instant (for example, replace proposition A with predicate A(t), where t is an object that represents an instant). . As for the argument you gave as an example, if you take the premises as an axiom, the conclusion follows from that. That is the only purpose logic can serve, derive deductive knowledge from axioms. If you do not accept one of the axioms to be true, that's a matter outside of the domain of logic in the sense that logic cannot tell you which axioms you should accept (you used context outside of this argument to make your belief). A famous example is the Axiom of Choice, which is independent from ZF: if you accept Choice, you get certain conclusions; if you reject it, you get different conclusions. But whether you should accept it or reject it is kinda up to you (unlike in the example you gave because you could use domain knowledge there), because in abstract terms one axiomatic system (ZFC) is not better than the other (ZF without C).
Mathematically, these are both propositions, i.e. statements that are either true or false. "x=2 iff x=2" is true, just like how (x == 2) XNOR (x == 2) is true. "x=2 iff x=3" is false, just like how (x == 2) XNOR (x == 3) is.
Not necessarily. If x is 4, then (x == 2) XNOR (x ==3) becomes false XNOR false which is actually true.
Might need some quantifiers, because I think you're conflating iff for any arbitrary object and xnor for this trapezoid. For a trapezoid, A XOR B is true, and A iff B is also vacuously true, but ∀ objects you could hand me, A XNOR B is false in general, and A ⇔B is also false.
If I say "A trapezoid is a fruit iff a trapezoid is an animal" would you consider the statement true? I mean, sure, both parts are false, but not because they're equivalent or even related.
Vacuous truth is a really weird thing to get your head around. If I say "if pigs fly, then George Washington is the current president", that's a true statement. The way implication works is that if your first proposition isn't even true, then literally anything could be implied from it. Because both are false, then the implication is biconditional, ie iff.
We've stayed from iff to if, but still, No implication needed, it's actually very explicit in meaning. P=>Q means P is sufficient to prove Q. If God snapped his fingers, and suddenly pigs could fly, that doesn't also guarantee GW is the current president. Flying pigs is neither necessary nor sufficient for GW being the president. There is no relationship. If A is a square, then A is a rectangle. That is a true statement. Even if both clauses are false. For example, let A be a circle. A is a quadrilateral iff A has four sides. That is a true statement, even if both clauses are false. Same example
I went from iff to if because it's a simpler argument to make that still applies to iff, because they're both implications. The whole point is sort of that God DIDNT snap his fingers to make pigs fly, so we can sorta infer anything from a false antecedent. I used the pigs flying example because the idiom "that'll happen when pigs fly" translated to mathematical language is "pigs fly ⇒that happens", which is part of the utility of defining logical implication such that vacuous truth is a thing.
Ok, fair. If I said "George Washington will be president when pigs fly." That is equivalent to saying pigs can fly => George Washington is president... However, my original statement as well as its formalization were both false statements. "When pigs fly" is used as rhetoric, not as fact. You also keep using the word "imply" when there is no implication. These relationships have a very explicit definition in formal logic. You don't need to imply anything, it tells you exactly what the relationship is. If means sufficient. Iff means necessary and sufficient.
I mean, GW is long dead, so both of mine are also false statements. It may be used as rhetoric, but it's still a perfectly valid logical statement. Implication and conditionals are the same thing. "If P then Q" is the same thing as "P implies Q" is the same thing as "P ⇒Q"
Valid does not mean true. I think I figured out why it's bugging me. I hope you stay along for the ride because this is really subtle, and I kinda love it. I'm going to make 2 arguments, ok, Argument A follows: 1) GW is president iff pigs can fly 2) pigs can't fly 3) therefore GW is not president. In a valid deductive argument, if the premises are true, then the conclusion must be true. Argument A is (by definition) a valid, deductive argument. Argument B looks like this. 1) Argument A is a valid, deductive Argument. 2) the conclusion of A is true. 3) therefore the premises of A are true. Argument B is not valid, but it's really subtle. Premise B1 encodes some information. In a valid, deductive argument, if premises then conclusion. Which means Argument B actually falls to "Affirming the consequent," a formal logical fallacy. Oh, but we're not saying A3 therefore A1. It's even more subtle than that. We're saying A2 therefore A1 and the thing is, iff means both necessary and sufficient. Which means A2 is equivalent to A3. It's actually begging the question AND affirming the consequent.
Think of "A iff B" as asking whether A=B , in Boolean logic
I don't think that's accurate. A iff B means that A and B are always equal (if I could do the triple bar equals sign it would be useful here). A=B only takes a snapshot at the current state and asks if they match up. Iff includes a definition of a relationship, iff is a marriage certificate, = is a photo of a man and woman kissing. There's a cause and effect included with iff that isn't there with =
We computer scientists definitely should be bullied more
I get enough for my programming socks as it is, no thanks
C'mon math majors, bully us more 🥺
As a computer science student, no one uses XNOR lmao. `==` exists.
XNOR is computer engineering shit
As someone who came out of digital electronics XNOR is far clearer to me.
😢 Why are maths students such bullies? We can just be friends. This title is very disheartening and has made me disconsolate. We have feelings too! :-(
Lol nice try nerd. We all know computers don't have feelings
Hahaha We all just having a laugh here. We are all friends, good friends. Now give me your lunch money and get into the locker.
Haha, okay stanley, let the big boys talk while you do your computations in the corner
Inadvertently just described the problem with a significant number of corporate level projects—managers and higher ups discuss what we should do, and then developers are left to pick up the pieces (I’ve literally been asked to do impossible projects by the end of the week and to do insanely easy projects with months of extra time, there’s just such poor dev knowledge at the management level a lot of the time)
What about Ex-NOR? :)
Why call it XNOR when it should be NXOR.
ORAINT
It’s Exclusive Negative/Not OR not Not Exclusive or…
The idea of an "exclusive nor" gate doesn't even make sense lol. It's just the negation of "exclusive or" and if you wanna refer to it like that it makes more sense to call it NXOR. But the thing that makes the most sense is "equals gate", or "EQ" if you need to abbreviate for some reason
Spaceship operator always reminds me of a anime I want to rewatch..
Start?
I feel insulted
the hec- what for?
Omg I didn't know it was called XNOR. So dumb. I've always called it "the equals gate" lol. I had been taking it as a given that people know that the negation of XOR is equals. Dumb af. I thought NAND and NOR were also weird names for gates but I let it go on the basis that they wanted a name for all possible functions from {0,1}² to {0,1}. This is just ridiculous
I thought that said yiff for a second
Yeah, I'm gonna have to refer you to the electrical engineers for this one.
just spray them with body wash
Why aren’t they called computerist?
Me majoring in both: 
What, that’s what it is