How is ordering numbers from least to greatest like putting spelling words in alphabetical order?

Answer 1

When you arrange the numbers from least to greatest you say that "the symbol "1" should be the first element in the list. And the symbol "2" should be the symbol for the number with the second smallest value" and so on. So what you do is assign symbols to to the numbers. These symbols can be arranged in a list according to the value each symbol gives. Since values are so closely related to numbers, this concept seems easy to grasp. Giving birth to the concept of decimals, we know that 1.2 should be between 1 and 2, and that 1.23 should be between 1.2 and 2.

The same thing can be done in an alphabet, but here you don't have any specific reason for the order of the list. With numbers, it's natural to say that 1 has a smaller value than 2, but for the alphabet, this isn't natural. There is no reason why one letter should have a different value than another, because letters don't have values naturally, like the numbers do. But now is the time to define this ourselves. The most common way to write the alphabet is a b c d... z, so since we know this list of letters by heart, we base our ordering on this list. So instead of saying "the element with the smallest value should have the symbol "1"", you say "the element with the smallest value should have the symbol "a"", and so on. Now we can also introduce "decimals" in our alphabetic list, saying "ab" should be between "a" and "b", and that "aab" should be between "a" and "ab".

So now the list of numbers and the list of letters have the same properties, concidering order. Even though you can't say that a + c = d, you can say that "a" has the lowest value in our alphabetic order, and "1" has the lowest value in our number based order. So with our order-system defined, these will behave the same way.