3. eli5: how can we intuitively prove that set N is countable although it is infini...

eli5: how can we intuitively prove that set N is countable although it is infinite.. how can it be countable?

Countable means that it’s possible to put the numbers in some kind of order. It may be infinite in size, but it’s possible to say “this is the first one, this is the second one, this is the third one.”

For an example, there are a countably infinite number of even numbers. You can say that the first one is 2, the second one is 4 and so on. If you wanted to know the 101st even number, you just need to double it and get 202. That relationship is what makes it countably infinite.

The reason this matters is because there are sets that aren’t countably infinite. An example of this would be all the partial numbers between 0 and 1. There’s no way to call say 0.01 the first or 0.02 the second, because there are an infinite number of values between those values.

/r/explainlikeimfive Thread
Previous
Next

Recently removed from /r/explainlikeimfive

Eli5 What’s the difference between declaring bankruptcy and just being broke? Eli5: How do music producers (Especially Hip Hop producers) sample a stem from a song without taking the rest of the song with it? ELI5: Why is a 12V battery in a car so dangerous to short circuit but a normal 12V battery is harmless? ELI5: How do our brains remember things? ELI5 Why do we feel pain and how does our body know when to stop feeling it? ELI5: How are you able to go to bed super hungry, but wake up the next morning and not feel the need to eat anything? ELI5: where is the ringing noise coming from with tinnitus?? can’t google because it thinks im asking how people get tinnitus… Eli5 - Why do shows like American Idol and The Voice have such a low rate of producing/finding people who can be a commercial success? ELI5: What are "deductibles" in the context of medical insurance? If you're paying insurance, why do you still get charged an often large part of your medical expenses when you have an accident? ELI5 is looking for new moderators! ELI5 How do alligators & crocs, too I suppose, swim underwater in sandy, marshy water and not react to sand getting in their eyes? eli5: In the days of muskets, why did armies March straight towards each others fire? ELI5: Why do certain countries have ridiculous amount of hydrocarbons(oil and natural gas) and the countries right next to them have virtually none? Eli5: what exactly is a virus and are viruses alive? ELI5: How does a variable-yield nuclear weapon work to allow the operator to control the strength of the explosion?

More Random Comments

This song is quite accurate. From Crazy Ex Girlfriend. So many good songs in that series, it was difficult to choose. But I just got mean-girled by some witch, so this should work:) If you had a button which would eliminate all human beings in an instant, would you press it? Gold Reserve Extract on top of pre-workout stack Oof this ones complicated Opinions on super likes? Do they come across as desperate? As a guy, I wouldn’t think it is weird to get one. How would you feel if you received a platinum SL with a message? I think the message could definitely help you stand out. I had this crazy thought THERE WON’T BE A #SAFEMOONSQUEEZE Thoughts on buying Level 3 books to study for Level 2 and Level 3. HSV2/ Risk - Communication Issue How do I avoid shallow women? How do I attract genuine ones? I am a muslim who genuinely have some questions and I hope you are peaceful in discussion Linux Timeline v20.10 U.K. Carrier Capability Returns To The Indo-Pacific RTX 3050 or RTX 2060? Months pass, unresolved tickets #818460 and #130113.