You know what だ and です are. You know the particles は and が. Now, it's time to learn about how to say "not" and how to say things in past tense.
Note: "X" is the subject/topic; "Y" is the description/quality that is not true.
Let's assume first that all examples in this lesson are in contexts in which we are talking about a topic and giving a statement that it is not such and such. So, we know that we have Xは. Now, we have だ and です so far for "is", and we only know the end form: しゅうしけい. So, we'll need to learn a new base to make the negative. This base is called the れんようけい.
|だ → で|
We only need to know the one for だ to make the negative. Politeness has to be reconfigured in the phrase because of this. Now that we have the starting point, we need to use an ending to finish what we've started. That ending as you say in the title of this lesson is ～ない. A lot of the world's words for not start with a n, so it should be easy to remember. But, we normally never use でない. Instead, we say ではない. ではない in speech often becomes じゃない, but it still means the same thing!
1a. That is a pen.
1b. That is not a pen.
(That) is not a dog.
Sentence Note: A secondary interpretation of 2 is "I am not a dog" because the subject is not stated and we don't have the actual context for this sentence.
Polite Negative Forms
To make a polite negative phrase, you have two options. You can simply add です to ～ない. When you do this, you aren't actually saying "is" again. In this case, です's meaning is just showing politeness. Or, you can use ～｛では・じゃ｝ありません. If you remember from Lesson 8 that だ comes from である and that it will be important to know this later on, the time is now. Polite conjugations using it are "more polite" than just using です. So, they are best used with people whom you should show more respect.
Form Note: We not only have ～ではありません, but there is also ～であります that you can use to make more polite "is" statements. Try using this and ～ではありません with your teacher!
Politeness Note: Using では is naturally more polite.
It's not a bug.
Lee-san is not a student.
No, it isn't.
So, to use ～た we need to use the れんようけい again. You will see over and over again that it is this single form of a verb that is used to make almost everything. This time, we'll need to learn the れんようけい of だ and です. We'll also need to learn how to say past tense for the "more polite" phrases. First, let's learn how to construct the れんようけい for だ and です when we use ～た.
|だ → だっ 〇 / で X → ＋ ～た → だった||です → でし → ＋～た → でした|
As you can see, だ has two forms for the れんようけい. So, don't use で with ～た. If it helps you remember what this base does, you can call it by the English name "continuative form". It just continues to tell you more about what's going on in the sentence. Now, what do we do about "not" and ～た. The same thing applies. We need to use the same form of ない that we used for だ and です.
|～ない → ～なかっ → ＋～た → ～なかった|
Now that you've learned how to construct the past phrases, we'll look at the plain, polite, and more polite past tense phrases for positive and negative sentences in the chart below.
△: Though this exists, it's really old-fashioned and not used anymore.
Variant Note: Some speakers use ～だったです rather than でした, but the latter is still felt by most speakers to be the most natural phrasing.
The last column is the hardest to explain with what we've learned up to now. But, the same things apply. We know what ～た attaches to. ～ます in ～であります shows politeness in verbs just like です shows politeness for other things. That's all what's going on!
That wasn't water.
Tanaka-san was not a teacher.
There were two Japanese people.
That over there was a school.
He was a kid.
Sentence Note: Past tense often is used to not mean the past but show confirmation, which is how Ex. 10 would most often be used for.