How did Greeks, Romans build the greatest civilization without the decimal number system?

I would respond by saying your figures are rubbish!! If you can only count to 4999 how can you tell if you have 8,000 men in your legion? Or how much bread you need to bake for a city? Or how many of the enemy face you? "Hail Caesar, there are 4,999 Gauls plus some extras attacking us!". Go back to books, not websites. You need to know what you are doing to write a book. Multiplication using the Roman system was possible,(I have done it) if cumbersome, but they used a "shorthand" mathematical system sometimes. You have also forgotten the Egyptians and their achievements. How do you think that they managed? Many Master Masons in the Medieval period built soaring cathedrals without the decimal system, and their cathedrals are still standing. You don't need a decimal system to achieve great things. It is a great help, yes, but not an essential. I build medieval siege engines. I don't use a ruler. I start off with a piece of timber and cut everything to that ratio that I need to fit together. The siege engines work. The Masons would design Cathedrals using The Great Circle, and it's ratios 2:4:8. They needed nothing else.

Who says it can only count up to 4999--plenty of ancient historians like Polybius and Livy mentioned bigger figures. The ancient numerical system was less efficient but that didn't preclude significant architectural etc achievements, although modern western advances greatly exceeded them.

Depending on the island/city and era the Greeks had a separate and more complex numbering system than the Romans and Greek was frequently used as a lingua franca in the Roman Empire.

Far too big a package of questions to even attempt to answer here ! The Roman numeral system was indeed extraordinarly clumsy and inefficient, allowing Addition and Subtraction of a sort, but NOT Multiplication and Division, which require the Arabic "zero" - "0". Don't get too "hooked" on decimals though - that system has ENORMOUS didsavantages. In no time, you run into long strings of figures, and in practical applications the fact the slightest misplacement of the "point", which is very easily done, causes a large-scale error - 10 times too little or 10 times too much, and that fact not at all obvious. This is particularly serious where medications are concerned, and many lives have been lost in consequence. "Vulgar Fractions" are often better, especially if used on the base of 16. This allows 'halving' down to 1 without any 'complications - 8,4,2.1 - and similarly upwards - 32, 64, 128 etc.with any error immediately apparent, and was in general use in Engineering for screw-thread sizes etc. It was also - and maybe still is ? - used in cases of shared ownership - for example, where a ship had several owners, each held so many "sixty-fourths. Incidentally, just before I left teaching I "sat in" on a Maths Class where the teacher was away. 16-year-olds, "University material", and doing the sort of mathematics where even the "worked example" in the text-book was incomprehensible to me. BUT - I observed that when they had to multiply 17 by 5, they all wrote down five sevnteens in a column and added them up ! When I queried this, it turned out that none of them had been allowed to learn - and chant - as I had - their Multiplication Tables when they were 6 years old and it was fun, because "they would learn them when they needed them". Of course they hadn't, and now were in the same position as the Romans ! They were quite amazed at the Mental Arithmetic skills which I could display, and rightly indignant that they'd never been allowed to acquire them.

Far too big a package of questions to even attempt to answer here ! The Roman numeral system was indeed extraordinarly clumsy and inefficient, allowing Addition and Subtraction of a sort, but NOT Multiplication and Division, which require the Arabic "zero" - "0". Don't get too "hooked" on decimals though - that system has ENORMOUS didsavantages. In no time, you run into long strings of figures, and in practical applications the fact the slightest misplacement of the "point", which is very easily done, causes a large-scale error - 10 times too little or 10 times too much, and that fact not at all obvious. This is particularly serious where medications are concerned, and many lives have been lost in consequence. "Vulgar Fractions" are often better, especially if used on the base of 16. This allows 'halving' down to 1 without any 'complications - 8,4,2.1 - and similarly upwards - 32, 64, 128 etc.with any error immediately apparent, and was in general use in Engineering for screw-thread sizes etc. It was also - and maybe still is ? - used in cases of shared ownership - for example, where a ship had several owners, each held so many "sixty-fourths. Incidentally, just before I left teaching I "sat in" on a Maths Class where the teacher was away. 16-year-olds, "University material", and doing the sort of mathematics where even the "worked example" in the text-book was incomprehensible to me. BUT - I observed that when they had to multiply 17 by 5, they all wrote down five sevnteens in a column and added them up ! When I queried this, it turned out that none of them had been allowed to learn - and chant - as I had - their Multiplication Tables when they were 6 years old and it was fun, because "they would learn them when they needed them". Of course they hadn't, and now were in the same position as the Romans ! They were quite amazed at the Mental Arithmetic skills which I could display, and rightly indignant that they'd never been allowed to acquire them.

I don't think anyone has a problem with India. I find Indian people very likable. And the Taj Mahal, what a testament of a mans love for his wife. I do have a problem with the caste system though. I believe everyone was created equal and nobody should be doomed to poverty just because they were born into the wrong caste. I also believe that America has so many professionals that are Indians is because this is the land of opportunity. And of coarse America is made up of people from every nation on earth for that very reason.

Depending on the island/city and era the Greeks had a separate and more complex numbering system than the Romans and Greek was frequently used as a lingua franca in the Roman Empire.

Who says it can only count up to 4999--plenty of ancient historians like Polybius and Livy mentioned bigger figures. The ancient numerical system was less efficient but that didn't preclude significant architectural etc achievements, although modern western advances greatly exceeded them.