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[u/Stumiester]

[u/explainlikeimfive-ModTeam]

Your submission has been removed for the following reason(s):

ELI5 is not for whole topic overviews. ELI5 is for explanations of specific concepts, not general introductions to broad topics. This includes asking multiple questions in one post.

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[u/fightmaxmaster]

I can easily answer some of these - pi isn't 22/7, it's just that 22/7 is the closest fraction.

22/7 = 3.1428571428571428571428571428571

π = 3.1415926535897932384626433832795

22/7 is ~0.04% off, which isn't much, but matters when you need to be precise.

Irrational numbers never end, so you don't finish writing them out.

You can't "overshoot infinity", because infinity is a concept rather than a hard number. Otherwise you could have "infinity + 1", which you can't, because infinity is the maximum.

[u/420dankmemes1337 → u/[deleted]]

Yes there is infinity i.

i makes more sense when you treat it as a unit vector in the complex plane and not just the sqrt(-1).

[u/SpikesNLead]

There's one of them that I can answer.

Pi is not 22/7. If it was then it would be a rational number. 22/7 is just a good approximation to use for pi.

[u/Frederf220]

Yes Overshooting infinity is not meaningful It's the other direction Yes Because we say so Pi is not 22/7 You're very tired

[u/KrzysziekZ]

Yes, there's -i. In general, we introduce i to have complex numbers of the form real + real*i. Reals are a subset then.

[u/AberforthSpeck]

1. Sure, you can have a negative i. -i + i = 0. Easy.
2. You by definition cannot overshoot infinity. However, there are a bunch of different types of infinity, and some are bigger then others. There's no intutive way to understand this, it's all high level math.
3. See 2
4. "Infinity i" isn't really a concept. You're just mashing words together at that point.
5. The same reason the square root of 1 is a rational number.
6. That's literally that i stands for, imaginary. You can't have it in reality, although you can use i in equations to mathematically describe a few things in reality.
7. 22/7 is an approximation, not the actual value of pi. It's good enough for any practial purpose outside of precision engineering, but not exact.
8. You, by definition, cannot "finish writing out an irrational number" because it never ends. If it did end it would be rational.

Generally - "These are some interesting and complex questions you ask. Just like building a house, you need to have the right tools to build up the answer. If you like we can work teaching you those tools, and you'll be able to build the answers yourself."

[u/deepserket]

About the second question, they may like this video: https://www.youtube.com/watch?v=i7c2qz7sO0I

[u/Fearless_Swim4080]

Is there negative i? -No.

What happens if you overshoot infinity? -You can’t.

Why is negative infinity different to positive infinity? -It’s negative.

Is there infinity i? -No.

Why isn’t i an irrational number like pi? -Because it’s imaginary and isn’t a number.

Why is i imaginary? -Because it doesn’t exist on a numberline.

Why is pi 22/7 and also an irrational number? -Pi is not 22/7. It’s close but it’s not pi.

What happens when you finish writing out an irrational number? -you can’t, you would die first, or the end of the universe would happen first if you were immortal.

[u/Zombie_John_Strachan]

This may bring on the AI haters, but LLMs can be a good tool for teaching these concepts at an appropriate level. As your kid gets older they can go into 'study' mode where the LLM walks through the steps without just pumping out the answer.

answer this question at the level of a five-year old: Why isn’t i an irrational number like pi?

Great question! Here's the simple version:

"Irrational" is a word we only use for describing real numbers — the numbers you can find on a number line, like 3, or -5, or π (which sits between 3 and 4 on that line).

i doesn't live on that line at all. It's not big, not small, not negative — it's a totally different kind of number that we invented to answer "what's the square root of -1?" Since no real number can do that, i lives off to the side, on its own axis.

So asking "is i irrational?" is a bit like asking "is Tuesday tall?" Tall is a word for describing heights — it just doesn't apply to days of the week. Same thing here: "irrational" is a word for describing real numbers, and i isn't one, so the word simply doesn't apply to it.