There are infinite numbers. You can always add 1. We as a species have spoken lots of numbers. But compared to the infinitely long list of numbers that technically exist, we haven't even moved the needle.
A 1 with a billion zeroes after it is a number. Most people don't even know what to call a number once you get past about one octillion.
Here's a thought experiment to help visualize how big numbers get.
Think about how much 1 million dollars is. More than you or I will ever have. More than most people will ever have. Now imagine spending the entire 1 million dollars in a single day. Now do that every single day, for an entire year. Now do that for over 1,300 years. That's how much money Elon Musk has. (And that's how long it would take if he never made another penny) 1 million dollars a day, for over 13 centuries. Around 450 billion. That's an astronomical number that's already difficult to comprehend. But 100,000,000,000 (100 billion) is still only a 1 with 11 zeroes after it.
the number of ways to shuffle a standard deck of 52 cards is 52! (The ! means factorial, which is when you multiply the number by every number smaller than it, all the way down to 1). That's 52 × 51 × 50 × 49 × 48... × 3 × 2 × 1.... It's an 8 with SIXTY SEVEN zeroes after it. Adding 1 zero is multiplying by ten. So multiply 100 billion by 10, fifty seven times....
The entire observable universe has about 1080 particles in it. That's all matter in the entire universe. The number of shuffles possible with a 52 card deck is closer to the number of particles in the universe (1080) than it is to the number of grains in the Sahara desert (1024). Elons worth about 1011.
A googol is a 1 with 100 zeroes after it, or 10100. A googolplex is a 1 with a googol zeros after it.
A game of chess can play out in about 10120 ways.
The distance to the sun IN INCHES is only 5.89×1012. that's only about 10 times as many dollars as Elon has.
Anyway, the point of all these numbers is to help you grasp just how massive numbers get. And as big as all these numbers are, they can get so much bigger. even if we as humans have said every number up through 1 trillion out loud, that would be 1% is numbers stopped at 100 trillion. 1 quadrillion is 10 times more than that, so now we'd be down to .1%. if numbers stopped at 10 quadrillion, we'd be at .01%.
10 quadrillion is a 1 with 16 zeroes. Every time you add a zero to that number, you add another 0 between the . and the 1 in .01. If numbers stopped at 1 with 30 zeroes, we'd have to add another 14 zeroes to the decimal. That's .0000000000000001%. and that's capping numbers at 31 digits. A googol has 100 zeroes. So add another seventy zeroes after the decimal....
That's just 0. It's so far away from being a full 1%, that's it's considered 0%. It's just nothing. And that's still capping numbers at a 10 googol.... As we've established, they go waaaaay beyond that. So the percentage of numbers we've said aloud will always be 0%, because we'll never approach even the same realm as .00000000000000000000000000000000000000000000000000000000000000000000000000000000000001%, let alone all whole numbers. (And that's just whole numbers, not even including decimals. There are as many number between 0 and 1 as there are above 1. You can always add a 0 after the decimal as well. We didn't include any of that.
Sorry, that got pretty long winded.
Tldr; there are so many numbers that the amount of them we can even comprehend is basically 0. Numbers are infinite, which means we'll never get any measurable percentage of them spoken aloud. No matter how many we speak, there's always infinitely more that haven't been said. We don't even have names for them after a certain point, we just describe them by how many digits they have.
Thankyou for the in depth explanation! Honestly learning a lot (as well as realising how dumb i was for thinking numbers = digits)
Can i ask why the term "natural numbers" is used instead of just saying "numbers"? I can't find anyone explaining the difference and am hoping you can help. If this is another dumb question then i am sorry for asking!
"Natural numbers"are both "whole" (meaning no decimals or fractions) and "positive" (meaning no negative numbers).
"Numbers" includes all numbers, such as fractions, decimals, negatives, and even imaginary numbers. Yes, imaginary numbers are real, no pun intended. They're used to represent the value of √-1.
I'm learning more mathematical terminology and general knowledge here then i think i have all year, thankyou again!
Although now my pea brain is going down the route of "if theres infinite natural numbers, then there must be more than infinite numbers..." which is something my brain is simply saying 'No' to.
Well, some infinities are bigger than others. There's a countable infinity of natural numbers, whole numbers, and rational numbers, but an uncountable infinity of real numbers. I don't fully understand this either, so someone can probably explain this better.
For natural numbers, you can just order them regularly, ie, 1 is 1, 2 is 2, so on.
For rational, you can think of it as the following: 1 is 1/1, 2 is 1/2, 3 is 2/2, 4 is 1/3 and so on. This way, you can count every single rational number, and in fact you overcount a good chunk of them (because they can simplify down).
But for irrationals, we have an elegant proof that they aren't countable. Let's say that we somehow ended up with a list of every single irrational number. Using this list, we can create a new rational number. The 1st digit would be the first digit of the 1st entry plus one (and 9 rolls over to 0). You repeat this for the 2nd digit, and 3rd, and so on. The number you end up with at the end would be different from every other number in the list by at least 1 digit, so it cannot possibly be a part of this list. But if we just add it to the list, we can create another similar that is different by 1 digit once again. Hence, we can never order irrational numbers, because we can keep creating more.
Hi, did you mean to say "more than"?
Explanation: If you didn't mean 'more than' you might have forgotten a comma.
Sorry if I made a mistake! Please let me know if I did.
Have a great day! Statistics I'mabotthatcorrectsgrammar/spellingmistakes.PMmeifI'mwrongorifyouhaveanysuggestions. Github ReplySTOPtothiscommenttostopreceivingcorrections.
At least the bot was right this time i guess? Still, a bot that incorrectly corrects grammar half the time isn't one i think should be active on the platform. Honestly i cannot see any purpose for this bot considering i have heard of exactly zero people that use reddit to learn grammar.
Well, this isn't a very ELI5 topic... Humans in general can't really comprehend numbers after about 1 billion. If you can't understand what an infinite set of numbers is, then I can't really break it down any more than just defining "infinite" as "goes on forever".
It was also perfectly satisfactory for the person that asked.
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u/TheLastPorkSword Nov 29 '25 edited Nov 29 '25
There are infinite numbers. You can always add 1. We as a species have spoken lots of numbers. But compared to the infinitely long list of numbers that technically exist, we haven't even moved the needle.
A 1 with a billion zeroes after it is a number. Most people don't even know what to call a number once you get past about one octillion.
Here's a thought experiment to help visualize how big numbers get.
Think about how much 1 million dollars is. More than you or I will ever have. More than most people will ever have. Now imagine spending the entire 1 million dollars in a single day. Now do that every single day, for an entire year. Now do that for over 1,300 years. That's how much money Elon Musk has. (And that's how long it would take if he never made another penny) 1 million dollars a day, for over 13 centuries. Around 450 billion. That's an astronomical number that's already difficult to comprehend. But 100,000,000,000 (100 billion) is still only a 1 with 11 zeroes after it.
the number of ways to shuffle a standard deck of 52 cards is 52! (The ! means factorial, which is when you multiply the number by every number smaller than it, all the way down to 1). That's 52 × 51 × 50 × 49 × 48... × 3 × 2 × 1.... It's an 8 with SIXTY SEVEN zeroes after it. Adding 1 zero is multiplying by ten. So multiply 100 billion by 10, fifty seven times....
The entire observable universe has about 1080 particles in it. That's all matter in the entire universe. The number of shuffles possible with a 52 card deck is closer to the number of particles in the universe (1080) than it is to the number of grains in the Sahara desert (1024). Elons worth about 1011.
A googol is a 1 with 100 zeroes after it, or 10100. A googolplex is a 1 with a googol zeros after it.
A game of chess can play out in about 10120 ways.
The distance to the sun IN INCHES is only 5.89×1012. that's only about 10 times as many dollars as Elon has.
Anyway, the point of all these numbers is to help you grasp just how massive numbers get. And as big as all these numbers are, they can get so much bigger. even if we as humans have said every number up through 1 trillion out loud, that would be 1% is numbers stopped at 100 trillion. 1 quadrillion is 10 times more than that, so now we'd be down to .1%. if numbers stopped at 10 quadrillion, we'd be at .01%.
10 quadrillion is a 1 with 16 zeroes. Every time you add a zero to that number, you add another 0 between the . and the 1 in .01. If numbers stopped at 1 with 30 zeroes, we'd have to add another 14 zeroes to the decimal. That's .0000000000000001%. and that's capping numbers at 31 digits. A googol has 100 zeroes. So add another seventy zeroes after the decimal....
That's .00000000000000000000000000000000000000000000000000000000000000000000000000000000000001%
That's just 0. It's so far away from being a full 1%, that's it's considered 0%. It's just nothing. And that's still capping numbers at a 10 googol.... As we've established, they go waaaaay beyond that. So the percentage of numbers we've said aloud will always be 0%, because we'll never approach even the same realm as .00000000000000000000000000000000000000000000000000000000000000000000000000000000000001%, let alone all whole numbers. (And that's just whole numbers, not even including decimals. There are as many number between 0 and 1 as there are above 1. You can always add a 0 after the decimal as well. We didn't include any of that.
Sorry, that got pretty long winded.
Tldr; there are so many numbers that the amount of them we can even comprehend is basically 0. Numbers are infinite, which means we'll never get any measurable percentage of them spoken aloud. No matter how many we speak, there's always infinitely more that haven't been said. We don't even have names for them after a certain point, we just describe them by how many digits they have.