```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 = ids.slice(startIndex, startIndex + limit);

  return {
    items: items,
    done: startIndex + limit >= ids.length
  };
}
```