```ts
export function mergeIntervals(intervals: [number, number][]): [number, number][] {
  if (intervals.length === 0) {
    return [];
  }

  // Validate input
  for (const interval of intervals) {
    if (!Array.isArray(interval) || interval.length !== 2) {
      throw new Error("Each element must be a two-number pair");
    }
    const [start, end] = interval;
    if (!Number.isFinite(start) || !Number.isFinite(end)) {
      throw new Error("Both start and end must be finite numbers");
    }
    if (start > end) {
      throw new Error("Start cannot be greater than end");
    }
  }

  // Sort intervals by start time
  const sorted = [...intervals].sort((a, b) => a[0] - b[0]);

  const merged: [number, number][] = [];
  let currentStart = sorted[0][0];
  let currentEnd = sorted[0][1];

  for (let i = 1; i < sorted.length; i++) {
    const [start, end] = sorted[i];
    
    if (start <= currentEnd) {
      // Overlapping or touching intervals - merge them
      currentEnd = Math.max(currentEnd, end);
    } else {
      // Non-overlapping interval - add the previous merged interval
      merged.push([currentStart, currentEnd]);
      currentStart = start;
      currentEnd = end;
    }
  }

  // Add the last interval
  merged.push([currentStart, currentEnd]);

  return merged;
}
```