```typescript
export function mergeIntervals(intervals: number[][]): number[][] {
  if (intervals.some(([start, end]) => start > end)) {
    throw new Error("Invalid interval: start cannot be greater than end.");
  }

  const sortedIntervals = intervals.slice().sort((a, b) => a[0] - b[0]);

  const result: number[][] = [];
  let currentInterval = sortedIntervals[0];

  for (let i = 1; i < sortedIntervals.length; i++) {
    const [start, end] = sortedIntervals[i];
    if (end >= currentInterval[0]) {
      // Merge intervals
      currentInterval[1] = Math.max(currentInterval[1], end);
    } else {
      result.push(currentInterval);
      currentInterval = [start, end];
    }
  }

  result.push(currentInterval);

  return result;
}
```