To Infinity and Beyond
There are an infinite number of numbers but there is a precise number of digits. There are 10 individual digits we call numbers that are numerals we equate to symbols which comprise the ten base numbers. Not one through ten but instead 0 thru 9. The ten base numbers are 0, 1, 2, 3, 4, 6, 7, 8, and 9.
There are no other digits but rather ways of accounting for numbers less than or greater than the placeholder of mathematics which is zero. We can add or subtract based on what those numbers represent when combined and we even recognize what we should or shouldn’t do based on how they are organized. If the brain couldn’t tell the difference you wouldn’t be able to read 1-10 as one through. If instead of 0-9 being read as zero through nine, in terms of the mathematics behind those symbols you would read it zero minus nine.
Zero represents a number that is a placeholder between the two derivatized and exponentiated versions of infinity, negative infinity and positive infinity. All numbers outside of the base 10 are simply symbols composed in such a format that they are understood as being representative of greater or lesser numeric values than other compilations of numbers. The number 0123456789 is actually rather redundant when spoken aloud as it reads because it starts with a zero. Simply placing a dot between zero and one in this case registers in the mind as that dot being representative of that particular number being decimated. Imagine the difference verbally if we were to say the number 0.123456789. Even reading that number you probably said zero point one two three etc.
Now imagine that number backwards. Written on paper the symbols would look like the following digit: 9876543210. The numeric value of those numerals as symbols when conjugated provide us with a digit linguistically identified as being nine billion eight hundred seventy six million five hundred forty three thousand two hundred and ten. Between you and I that’s still a number with only ten digits (0-9) we just know how to describe those digits being in that particular order as not being the same number as 0.123456789.
Now let’s explain an effect of that normally lost on people as to the importance of zero being not only a placeholder but representing an actual value as well.
Most equations are written in terms of using various symbols other than numbers to encapsulate the idea behind what function all the symbols within that particular equation does. When writing out the ideas behind mathematics in word form the ideas behind the symbols we all know and love become almost comically easy to grasp.
It is the actual calculation that is far more strenuous to recognize in any given series of complex mathematical calculations and boiling the value down to simple words. The words identifying a number with a function identify the numeric path necessary to reach an outcome.
I would say phenomenologically the idea of values manifests quite differently in the mind than the actual mathematics required to achieve any given result on paper. One plus one equals two a million plus a million equals two million and a quintillion plus a quadrillion equals one quintillion one quadrillion. Those 24 words alone describe all of the mathematics necessary to achieve a value representative of being 1,000,000,000,000,000 more than 1,000,000,000,000,000,000. But if I were to just present the two numbers as being separate values with an addition sign between them they almost seem the same. But in terms of how many digits there are between them and the value difference in them they couldn’t be further apart.
They have values that when compared to one another are 1,000 orders of magnitude in difference from one another. To count the numbers between the two as a whole would require reading from lowest to highest and require starting at one quadrillion or 1,000,000,000,000,000. The next number if counting up to one quintillion one digit at a time would be one quadrillion one, then one quadrillion two so on and so forth. In number form that is the same conceptually as counting from zero to one to two. But writing out the steps to achieve those three numbers in terms of simply counting them is equivalent to saying the following three numbers
1,000,000,000,000,000
1,000,000,000,000,001
1,000,000,000,000,002
To get from one quadrillion up to one quintillion one would have to count all the numbers starting at 1,000,000,000,000,000 all the way up to 234,567,890,987,654,321 and that would still be less than a quarter of the way there. To count to a quintillion until one digit away we would have to count every number between one quadrillion and 999,999,999,999,999,999 to finally have the next number in the count to be one quintillion.
Just to clarify even more so how massive that difference is between one quintillion and one quadrillion note that in their written format, the difference between the two numerals is nine hundred ninety nine quadrillion nine hundred ninety nine trillion nine hundred ninety nine billion nine hundred ninety nine million nine hundred ninety nine thousand nine hundred and ninety nine.
If you didn’t notice the pattern linguistically, after we hit nine we started to name the numbers based on each additional digit's previously conjugated linguistic transliteration. 99 is ninety nine. 999 is 9 hundred and ninety 9.
The importance of understanding mathematics cannot be understated. It is important to recognize the difference between these various terms not only linguistically but their numeric value as well mathematically.