Ni faris buĝeton sen ke ni forgesis la imposton.

Sen ke means without followed by a whole clause.

So:

• sen = without
• ke = introduces a subordinate clause, roughly that

In this sentence, sen ke ni forgesis la imposton means something like without our forgetting the tax.

A shorter and often more natural Esperanto version is:

• Ni faris buĝeton sen forgesi la imposton.

That uses sen + infinitive instead of sen ke + full clause.

It is understandable, but many speakers would probably prefer a simpler version:

• Ni faris buĝeton sen forgesi la imposton.

Why?

Because the subject is the same in both parts: ni in ni faris and ni forgesis. When the subject stays the same, Esperanto often prefers the shorter infinitive construction.

So:

• understandable: Ni faris buĝeton sen ke ni forgesis la imposton.
• more natural for many speakers: Ni faris buĝeton sen forgesi la imposton.

The sen ke version is especially useful when you want or need a full clause, for example if the subject is different.

Because after sen ke, you have a full subordinate clause, and a full clause normally needs its own subject and verb.

So in:

• sen ke ni forgesis la imposton

the clause has:

• subject: ni
• verb: forgesis

English often lets us avoid repeating the subject with without forgetting, but Esperanto only avoids the repetition if you switch to the infinitive version:

• sen forgesi la imposton

So:

• sen ke ni forgesis... = full clause, subject repeated
• sen forgesi... = no separate subject stated

No.

Sen already carries the idea of absence or negation, so you do not normally add ne for this meaning.

Correct idea:

• sen ke ni forgesis la imposton = without our forgetting the tax

If you said:

• sen ke ni ne forgesis la imposton

that would literally mean something like without our not forgetting the tax, which is not the intended meaning.

So for English speakers, the key point is:

• English: without forgetting
• Esperanto: sen forgesi / sen ke ...
• not: sen ke ... ne ... for this meaning

Because they are direct objects.

In Esperanto, the direct object usually takes -n.

Here:

• faris buĝeton = made a budget
  
  • buĝeton is what was made
• forgesis la imposton = forgot the tax
  
  • imposton is what was forgotten

So the -n ending shows what receives the action.

This is one of the most important patterns in Esperanto syntax.

La marks the noun as definite: the tax rather than just a tax or tax in general.

In context, this suggests a specific tax that the speakers already have in mind, probably one that belongs in the budget.

So:

• imposton = a tax / tax
• la imposton = the tax, a specific one

Whether la is needed depends on context. If the tax is already known or understood, la is natural.

Because the whole sentence is describing a past situation.

• Ni faris = we made
• ni forgesis = we forgot

Even though the clause is inside sen ke, it is still a clause with its own verb, and that verb gets a tense.

That said, learners should know two things:

• the sentence as written is understandable
• many speakers would avoid this issue by saying sen forgesi la imposton

You may also encounter sen ke with other verb forms depending on nuance, but for everyday learning, the safest takeaway is:

• full clause: sen ke
  • subject + finite verb
• simpler same-subject version: sen
  • infinitive

Yes — and for many speakers, that is the best version here.

So this is very natural:

• Ni faris buĝeton sen forgesi la imposton.

It is shorter and smoother because the subject is still ni.

A useful rule of thumb:

• same subject in both parts -> often use sen
  • infinitive
• different subject, or if you want a full clause -> use sen ke

For example:

• Ni faris buĝeton sen forgesi la imposton.
• Ni faris buĝeton sen ke la librotenisto forgesu la imposton.

In the second one, the subject changes, so a full clause makes more sense.

The special letter here is ĝ.

• ĝ is pronounced like the g in gem, giant, or judge-like sounds, depending on accent
• buĝeto sounds roughly like boo-JEH-to

Breaking it up:

• bu = boo
• ĝe = like je in Jeff
• to = to

And buĝeton is just buĝeto plus the object ending -n.