Necessity of judgment day, as viewed by the holy Quran

We as Muslim believers believe that all men and women will be raised up in a certain day after death. They all will be judged, and those who are good and virtuous shall live in PARADISE, and the sinners will join the fire of HELL.
We (according to some traditions) consider this world as a bridge that man should pass it over so as to join an eternal life; in other words, it is a farm to seed here and to harvest in hereafter, or in some verses of the holy Quran, this world is considered as a market where we can provide for the next life to come, as God says:

O you who believe, may I offer you a trade which will save you from a painful punishment? Come to believe in God and His Messenger, and strive for God's cause with your possessions and your lives. That will be better for you, if you only knew. [1]

Reasons for proving hereafter

The occurrence of the day of judgment is very clear, because:
1 it can be easily seen that this mortal life cannot be a reasonable object, and the final goal for such a creation; to come and live here for a period of time, living with immense hardships and difficulties, and end to nothing or to some dusts! Is that what is meant by our complex creation?

The holy Quran, addressing those who doubt about the resurrection asks: how do they doubt the power of the Almighty to raise the dead? While they already have seen God’s first creation?

The holy Quran says:

Do you think that we have created you for nothing (in jest), and that you will not be brought back to us?’ [2]

2 In this world the evildoers are usually in one line with the good ones and sometimes even higher; a non-equity which does not read with the great justice of God. So there must be somewhere to distinguish bad from good and false from truth, a place where everyone should see the result of their deeds.
God says in the Quran:

Do those who have perpetrated evil deeds suppose that We shall treat them like those who have faith and do righteous deeds, their life and death being equal? How bad is the judgment that they make! [3]

3 the infinite mercy of God necessitates that his mercy and bounties does not come to an end by death.
It reads in the Quran:

Say, ‘To whom belongs whatever is in the heavens and the earth?’ Say, ‘To Allah. He has made mercy incumbent upon Himself. He will gather you on the Day of Resurrection which is certain to come. Those who have ruined their soul will not come to believe. [4]

The holy Quran, addressing those who doubt about the resurrection asks: how do they doubt the power of the Almighty to raise the dead? While they already have seen God’s first creation?
He (the unbeliever) draws comparisons for us, and forgets his own creation. He says, ‘Who shall revive the bones when they have decayed?’ say:

He who created them for the first time will give them life again, and He has knowledge of all creation. [5]

Besides that; is the creation of man important in comparison with that of heavens and the earth? He who was able to create such a vast, and strange world, is he not able to raise the dead?
The holy Quran says:

Do they not see that Allah, who created the heavens and the earth and [who] was not exhausted by their creation, is able to revive the dead? Yes, indeed He has power over all things. [6]

[1] يَا أَيُّهَا الَّذِينَ آمَنُوا هَلْ أَدُلُّكُمْ عَلَىٰ تِجَارَ‌ةٍ تُنجِيكُم مِّنْ عَذَابٍ أَلِيمٍ ﴿10﴾ تُؤْمِنُونَ بِاللَّـهِ وَرَ‌سُولِهِ وَتُجَاهِدُونَ فِي سَبِيلِ اللَّـهِ بِأَمْوَالِكُمْ وَأَنفُسِكُمْ ۚ ذَٰلِكُمْ خَيْرٌ‌ لَّكُمْ إِن كُنتُمْ تَعْلَمُون َ(11)
[61:10,11]
[2] أَفَحَسِبْتُمْ أَنَّمَا خَلَقْنَاكُمْ عَبَثًا وَأَنَّكُمْ إِلَيْنَا لَا تُرْ‌جَعُونَ
[23:115]]
[3] أَمْ حَسِبَ الَّذِينَ اجْتَرَ‌حُوا السَّيِّئَاتِ أَن نَّجْعَلَهُمْ كَالَّذِينَ آمَنُوا وَعَمِلُوا الصَّالِحَاتِ سَوَاءً مَّحْيَاهُمْ وَمَمَاتُهُمْ ۚ سَاءَ مَا يَحْكُمُونَ
[45:21]
[4] ل لِّمَن مَّا فِي السَّمَاوَاتِ وَالْأَرْ‌ضِ ۖ قُل لِّلَّـهِ ۚ كَتَبَ عَلَىٰ نَفْسِهِ الرَّ‌حْمَةَ ۚ لَيَجْمَعَنَّكُمْ إِلَىٰ يَوْمِ الْقِيَامَةِ لَا رَ‌يْبَ فِيهِ ۚ الَّذِينَ خَسِرُ‌وا أَنفُسَهُمْ فَهُمْ لَا يُؤْمِنُونَ
[6:12]
[5] وَضَرَ‌بَ لَنَا مَثَلًا وَنَسِيَ خَلْقَهُ ۖ قَالَ مَن يُحْيِي الْعِظَامَ وَهِيَ رَ‌مِيمٌ ﴿78﴾ قُلْ يُحْيِيهَا الَّذِي أَنشَأَهَا أَوَّلَ مَرَّ‌ةٍ ۖ وَهُوَ بِكُلِّ خَلْقٍ عَلِيمٌ ﴿79﴾
[36:78,79]
[6] أَوَلَمْ يَرَ‌وْا أَنَّ اللَّـهَ الَّذِي خَلَقَ السَّمَاوَاتِ وَالْأَرْ‌ضَ وَلَمْ يَعْيَ بِخَلْقِهِنَّ بِقَادِرٍ‌ عَلَىٰ أَن يُحْيِيَ الْمَوْتَىٰ ۚ بَلَىٰ إِنَّهُ عَلَىٰ كُلِّ شَيْءٍ قَدِيرٌ‌
[46:33]