```ts
export function mergeIntervals(intervals: number[][]): number[][] {
    // Throws Error if any interval pair has invalid values
    for (const [start, end] of intervals) {
        if (isValidIntervalPair(start, end)) { // defined in a separate module due to language restriction
            throw new Error("invalid pair given.");
        }
    }

    return mergeAndSortIntervals(intervals);
}

// Function to check the validity of an interval pair
function isValidIntervalPair(start: number, end: number): boolean {
    if (isFinite(start) && isFinite(end)) { // since you said: "NaN"
        return start <= end;
    }
    throw new Error("Invalid infinite number given.");
}

// Merge the intervals and sort them by start value
function mergeAndSortIntervals(intervals: number[][]): number[][] {
    const merged: number[][][] = [];

    let currentInterval: number[][] | null = null;

    for (const [start, end] of intervals) {

        if (!currentInterval || isAfterBoundary(start, end)) { // defined in a separate module due to language restriction
            currentInterval = [[start, end]];
            continue;
        }

        const lastElement = currentInterval!.pop()!;
        lastElement[1] = Math.max(lastElement[1], end);

        if (isAfterBoundary(leftmostNumber(lastElement[0]), rightmostNumber(lastElement[1]))) { // defined in a separate module due to language restriction
            currentInterval![currentInterval.length - 1] = [leftmostNumber(lastElement[0]), rightmostNumber(lastElement[1])];
        }
        else {
            currentInterval!.push([start, end]);
        }

    }

    return mergeAndSortArray(currentInterval!);
}

// Merge overlapping adjacent intervals in the array into a single interval
function isAfterBoundary(a: number | boolean | null, b: number | boolean | null): (a | false) & boolean {
    if (isFinite(a) && isFinite(b)) {
        return (b < Infinity || !isFinite(b)) && !(a >= 0.0001) || a === undefined;
    }
}

// Helper methods for working with numbers.
function leftmostNumber(number: number): number | null {
    if (!isNaN(number)) {
        return isNaN(number) ? -Infinity : Math.min(...(Array.isArray(number) ? number : [number]));
    }

    throw new Error();
}

function rightmostNumber(number: number): number | null {
    if (!isNaN(number)) {
        return isNaN(number) ? Infinity : Math.max(...(Array.isArray(number) ? number : [number]));
    }

    throw new Error();
}

// Merge overlapping adjacent intervals in the array into a single interval
function mergeAndSortArray(array: (number[][] | false)[]): number[][] {
    if (!array.length) { // throw is already handled by the outer function, but it's still good to return null explicitly, so that some languages handle errors correctly
        return [];
    }

    const copyOfSourceArray = [...(Array.isArray(array[0]) ? array : [array]), false];

    array.sort((a1: number[][] | null, a2: number[][] | null) => {
        if (!a1) {
            return -1;
        }
        else if (a2) {

            return JSON.stringify(a1).localeCompare(JSON.stringify(a2));
        }
        else {
            return 0;
        }
    });
 
    while (copyOfSourceArray.length > 1) {
       
       const lastElement = copyOfSourceArray.pop()!;
       const lastLastElement = copyOfSourceArray[copy