אני כותבת לעצמי פתק, כדי לא לשכוח.

Because the speaker is feminine singular.

With אני in the present tense, Hebrew usually shows the speaker’s gender in the verb:

• אני כותב = a man/boy is speaking
• אני כותבת = a woman/girl is speaking

So this sentence is being said by a female speaker.

It can mean either one, depending on context.

Hebrew present tense often covers both:

• simple present: I write
• present progressive: I am writing

So אני כותבת לעצמי פתק could mean:

• I write myself a note
• I’m writing myself a note

Context tells you which is more natural.

Because Hebrew does not use a separate present-tense form of to be in normal sentences like this.

In English, you say I am writing.
In Hebrew, the present-tense verb form כותבת already does the job.

So:

• אני כותבת = I write / I am writing

There is no extra word for am here.

לעצמי means to myself or for myself.

It is made from:

• ל־ = to / for
• עצמי = myself

In this sentence, it means the speaker is writing the note for her own use, so the idea is something like I’m writing myself a note.

פתק means a note, slip of paper, or short written reminder.

It usually refers to something brief, not a long letter or document.
So it fits very well in a sentence about writing something so you do not forget.

Because פתק is indefinite here: it means a note, not the note.

In Hebrew, את is used before a definite direct object.

So:

• אני כותבת פתק = I am writing a note
• אני כותבת את הפתק = I am writing the note

Since this sentence has פתק without ה־, it is indefinite, so there is no את.

כדי introduces a purpose: it means so that or in order to.

So:

• כדי לא לשכוח = in order not to forget

It tells you why the speaker is writing the note.

Because after כדי, Hebrew normally uses the infinitive.

So the pattern is:

• כדי + infinitive
• כדי לזכור = in order to remember
• כדי לא לשכוח = in order not to forget

Here, לשכוח is the infinitive to forget.
The word לא simply negates it: not to forget.

By default, it is understood to be the same subject as in the main clause.

So in:

• אני כותבת לעצמי פתק, כדי לא לשכוח

the natural understanding is:

• I am writing myself a note
• so that I do not forget

Hebrew often leaves that subject unstated when it is obvious from context.

Yes. Hebrew word order is fairly flexible, especially with a purpose phrase like כדי לא לשכוח.

For example, you could also say:

• כדי לא לשכוח, אני כותבת לעצמי פתק.

That puts more emphasis on the purpose first.

The original order sounds very natural:

• first the action
• then the reason for it

The comma separates the main action from the purpose phrase.

So the structure is:

• אני כותבת לעצמי פתק = main clause
• כדי לא לשכוח = purpose

In modern Hebrew, punctuation can vary a bit, and you may sometimes see this kind of sentence without a comma too. But the comma here is perfectly normal and helps readability.

The infinitive is לשכוח, meaning to forget.

In Hebrew, infinitives usually begin with ל־, which often corresponds to English to:

• לכתוב = to write
• לזכור = to remember
• לשכוח = to forget

So in כדי לא לשכוח, the ל־ is just part of the infinitive form.

A male speaker would say:

אני כותב לעצמי פתק, כדי לא לשכוח.

The only change is:

• כותבת → כותב

Everything else stays the same.