```ts
export function keysetPage(ids: number[], cursor: number, limit: number): { items: number[]; done: boolean } {
  if (!Number.isInteger(limit) || limit <= 0) {
    throw new Error('Limit must be a positive integer');
  }
  if (!Number.isInteger(cursor)) {
    throw new Error('Cursor must be an integer');
  }
  for (let i = 1; i < ids.length; i++) {
    if (ids[i] <= ids[i - 1]) {
      throw new Error('Ids must be strictly increasing');
    }
  }

  const startIndex = ids.findIndex(id => id > cursor);
  const items = startIndex !== -1 ? ids.slice(startIndex, startIndex + limit) : [];
  const done = items.length < limit;

  return { items, done };
}
```