According to a Egyptian legend , the god Seth he had torn out the left eye of the god Horus and had torn him to pieces, but the god Thoth he managed to reassemble it thanks to his magic and his own magic allowed him to steal a fragment of the eye without, however, the absence of him undermining the integrity of the eye.
This legend, or if you prefer this myth, is considered by many to be the "point of origin of Egyptian arithmetic" and of the infinitesimal calculus, in fact, the parts of the eye of Horus (later identified as the eye of Ra) they were used to describe the fractions and together they represented unity, however it was an approximate unit, given the absence of a fragment that disappeared thanks to the magic of the god Thoth.
As a whole, the eye represents the sum of the first 6 values of the numerical series 1/2 ^ n, the sum of which, in modern mathematics, is equivalent to the decimal number 0.984375, also expressible as 63/64 , but in Egyptian mathematics, the sum of these elements gave as a result 1, or better, gave as a result 63/64 however, thanks to Thoth's magic this partial "unity" could take on the features of an integer, becoming 64/64 , in short, the magic of the god Thoth added the missing 1/64. 
Today we know that by removing the constraint of the first five elements and proceeding by adding all the infinite fractions obtained by halving the whole number, we would get closer and closer to unit 1 without ever actually reaching it, in fact we will find ourselves faced with a function expressed as the summation 1 / n ^ 2 ( ∑ 1/2 ^ n ) where n goes from 1 ad ∞ and whose result, given precisely by the sum of all the elements that make up the numerical series (therefore (1/2) + (1/4) + (1/8) + (1/16) + (1 / 32) + (1/64) +… ) will be a number that converges (in mathematics , convergence it is the property of a certain function or sequence of possessing a finite limit of some kind, or, the result of which as the variable or index tends towards certain values at a certain point or to infinity) around 1.
The fact that for the Egyptians ( 1/2) + (1/4) + (1/8) + (1/16) + (1/32) + (1/64) did not actually give 1 but it was very close and that the difference between 1 and 0.984375 (i.e. 0.015625) was a number so small that it could be overlooked, but not ignored, it gives us very precise information on the level of decimal accuracy possessed by the Egyptians, an accuracy that went at least up to 63/64 and that 1/64 that remained out, represented by a decimal with six digits after the comma, which was considered "negligible" , and it was negligible because, for those who were the observation tools of the time, it represented an extremely small value, the presence or absence of which would have had no visible effects, however, in the presence of more accurate observational tools or for special needs, it was possible to advance with the fractionation, thus reaching an ever greater level of accuracy.
Pretending to use a mathematical language , we could say that the observed parts of the eye of Horus are part of a certain whole, but to find the missing part we need to extend the search to a "wider" set and invisible to the human eye, defined by the magic of Thoth. Applying this kind of reasoning to modern mathematics, the risk of resorting to dangerous paradoxes is not negligible, however, by maintaining a lower level of accuracy and filling in the gaps with "Thoth's magic" , the mathematical logic of the Egyptians managed to evade those paradoxes.
This observation suggests that the Egyptians were able to perform much more accurate calculations, with an error of less than sixty-fourth and if the minimum value present in the eye of Horus was represented precisely by 1/64, this did not automatically mean that 1 / 64 was the minimum value known by the Egyptians, indeed, by applying the same logical procedure that led to the value of 1/64 it was potentially possible to proceed to infinity. But let's go in order.
The eye of Horus is a very recurring element in Egyptian archaeological finds, this element has enormous value, not only on a mathematical level, but also and above all on a religious level, and it is precisely in the myth of the eye of Horus that we can identify an additional mathematical element.
As we know, according to Egyptian mythology, the god Seth destroyed the left eye of Horus which was then recomposed by the magic of Thoth. The fact that the myth specifies that it is the left eye and that we are not given any information about the right eye of Horus coupled with the fact that in no myth we are told that the god Horus was a one-eyed god, means that somewhere part there must also have been a right eye of Horus and in fact, there is no shortage of finds depicting the right eye of Horus, and among the many, one find in particular has caught the attention of the mathematics scholars of the Egyptians, it is the stele by Nebipusesostri, dating back to the reign of Amenemhet III , in the central column of which the two eyes of Horus are depicted and not only those.
The really interesting element from the mathematical point of view, are not the two eyes, but the 'union of the two eyes and in particular the element that stands between the two eyes, these are three parallel symbols, often referred to as "tears of Horus" located below the eyes and placed exactly between the two mirror symbols that indicate the value of 1/64.
If we proceed, we assign the central symbol of the three the value 1/64 and the two external symbols the value 1/128 and then we add these numbers we will obtain 2/64, or 1/64 for each of the two eyes of Horus, exactly the missing value at all. 'one and the other eye to achieve mathematical unity and consequently those symbols could be read as a representation of the external set indicated by the “magic of Thoth”.
This mathematical interpretation, although interesting and fascinating, suffers from a profound logical defect which consists in having assigned three identical symbols of different values, this mathematical operation appears to be too artificial and forced. More likely the three symbols identified as the three tears of Horus had a unique value and their fractionation produced three elements of equal value. Proceeding with this observation it can be deduced that the tears of Horus as a whole had a value of 3/128 and separated, each of the three tears assumed a value of 1/128. Thinking in these terms, however, a further problem emerges, or rather, the problem of the eye of Horus returns, since it is not possible to achieve unity, as by assigning the symbol with the value 1/128 on the right to the right eye and the placed on the left of the left eye, we would find ourselves in the previous situation, that is with a value of the single eye equal to 127/128 and consequently, each of the eyes would be missing 1/128, and if it is true that in the hieroglyph there is still a symbol with a value of 1/128, it is also true that to complete the two eyes you need 2/128, consequently it is possible to complete the unit for a single eye, presumably the right one, while the other left eye will continue to be kept together by Thoth's magic alone.
However, there is an apparent mathematical way out, you can proceed with the division of the last tear into two parts, both with a value of 1/256 that will join, one in the right eye and one in the left eye. In this way the problem would not really be solved, as the sum of all the elements of a single eye would result in 255/256 and therefore both eyes would once again be missing a fragment, albeit an extremely smaller one. This situation, or rather, the presence of the third tear, suggests that it is possible to infinitely halve an integer, but at the same time it also tells us that this operation is negligible since it is "useless" to halve an integer more than 7 times, and 1/128 is precisely the seventh fraction of the whole, this fraction can also be expressed as 1/2 ^ 7.
Returning to the tears of Horus, as we have seen, their presence suggests once again that the Egyptians had a much more advanced knowledge of infinitesimal mathematics than one might imagine. As we know, this concept which would have subsequently evolved and spread up to the present day and I think it is appropriate to mention what is most likely the most famous example of this type of mathematics in the " Western world. “ .
As for Egypt we do not know exactly how far their mathematics went, the eye of Horus tells us that they knew extremely small numerical values and this means that they were able to perform extremely complex and accurate calculations. Unfortunately, however, their knowledge of infinitesimal mathematics helped lay the foundations of "advanced mathematics" of the Western world (in particular the Greek and Roman world) whose origins, at least as regards the “infinitesimal calculus” they sink only in Greece of the 5th century BC where the philosopher Zeno of Elea, to defend the theses of his teacher Parmenides , who argued that the movement was an illusion, elaborated the famous paradox of Achilles and the tortoise, also known as the paradox of Zeno, in which Achilles, chasing the tortoise will never be able to reach it.
The mathematical explanation of Zeno's paradox lies precisely in the fact that the infinite intervals traveled by Achilles each time to reach the tortoise become smaller and smaller and the limit of their sum converges for the properties of the geometric series. In this case Zeno observes that a sum of infinite elements, or rather, the limit of a sum of infinite elements is not necessarily infinite and a concrete example of this theory is given by the sum of the fractions obtained by halving an integer each time ( similarly to what would happen by prolonging the succession of the eye of Horus) , hence ∑1 / n ^ 2.
If Achilles in reality were absolutely able to reach the tortoise, from a mathematical point of view he would never have been able to reach it and when a mathematical function is in a situation of this type, it is said that it tends to a given value, in this case 1, that is, it gets closer and closer to 1 without ever reaching it. Having this level of mathematical knowledge implies the knowledge of the concept of infinitesimal, or of a numerical value that tends to zero but never reaches it.