"That is not right."
I'm not sure what's going on here. ちがいます doesn't seem negated, does that imply it actually means 'that is wrong'?
It's negative in meaning, not grammar. So yes, "That is wrong" would be a more accurate translation. 違い (chigai) literally means "difference, discrepancy" so ちがいます comes to something like "What you're saying is different from the truth", as far as I can tell.
ちがいます [違います] is actually a verb here in polite present form that means roughly "to differ (from), to vary." Therefore it does not have to be negated.
What's the difference between "chigaimasu" (no jap keyboard, sorry) and "chigaimasuyo"? Does the latter mean "that is right?" or do they mean the same thing ("that is wrong")? And I thought "that is right" is "soudesu" so I'm a bit confused
The よ on the end is actually a particle. Here it would be used to add emphasis, or impart new information. So ちがいますよ means the same thing overall as ちがいます, just with a bit of nuance.
Here's a link that talks about the two major ending particles: http://www.punipunijapan.com/japanese-particles-yo-ne/
And そうです can mean "That's right", too. Probably literally closer to "That's so," if you want to be more specific.
Im not a hundred percent sure but i do know that "yo" means you know. So chigaymasuyo means thays not right you know.
The first Japanese class I ever had the teacher would also say "だめです" to mean "not right". I understand it's more like an admonition - "don't do that", but it seems like it should be an accepted alternative in the right context.
Agree with Amelia. Chigau is a verb, and chigai is an adjective. There are adjectives ending with an -i or -na. But, I wonder can Chigai really can be a Noun? Amelia? Anyone?
Be careful with this one ! :) ちがい looks a lot like an i-adj, but isn't one. It is a noun.
On a somewhat more advanced note, it's also the stem of the verb ちがう. You can get the stem of a verb by looking at the ~ます form and dropping the ~ます. So, the ちがいます stem is ちがい, たべます is たべ, のみます is のみ. I don't know that this is immediately useful here on Duolingo, but you do see these stem forms pop up in some grammatical constructions.
It should be ちがう (adj). Because ちがい (n) means "difference". But still that would just translate "it is wrong". それ わ ただしい ません Is what translates "that is not right (correct)"
Actually, ちがう is a verb. It's just the casual form of ちがいます. You can sometimes use it to modify nouns, like how in English "to jump" is a verb, but in "the jumping frog" it modifies a noun.
In your second sentence, ただしい is an adj, so it should conjugate as ただしくありません. The whole sentence should read, それはただしくありません. So you may notice I've changed the final い to a く and had to add the verb あります to negate the adj. ~ません is how you make a verb negative (in polite form), but it's only for verbs.
Semantically, as someone else noted in this thread, ちがいます literally means "to be different". It's just also often used in a context of, "That's different (from reality)." So "not right" probably comes closer to the literal meaning than "wrong", but translating it you could probably either.