∞ and NaN

Not true. Also, @luna.judah said that 0^0, 1/0, and the 0th root of a number involve infinity, but I don't know how that could be.

Okay, so, you know how some people say 0/0 is undefined? Of course you'd know that, because it's a popular saying: Never divide by 0.

The way we get 0/0 is by looking at other fractions. We know that anything divided by itself is equal to 1, no matter what number you use. 1/1 is 1, 2/2 is 2, even 1,000,000/1,000,000 is just 1.

This means that 0/0 is equal to 1, right? Okay, now that we have this, let's put it into an equation. If 0/0 is equal to 1, then 0/0 + 0/0 is equal to 2, right?

But...if we add both numerators...we get 0, meaning that 0/0 + 0/0 is still equal to 0/0. But...0/0 + 0/0 is equal to 1 + 1, which is 2, not 1, which is what we got with 0/0! We've reached a paradox here.

Uh, 0/0 doesn't equal infinity, it's UNDEFINED because if 0/0 = x, then x times 0 = 0, but that's true with every number.

As for 0^0, same thing - anything to the power of 0 is equal to 1. 1^0 is 1. 5^0 is still 1. What about 0^0?

This means that 0^0 + 0^0 is...2! Wait, that makes ZERO sense, how can 0^0 be equal to 1, but 0^0 + 0^0 equal to...2?!

Wait I didn't say 0/0 was infinity. I just said that "we reached a paradox". I guess you could say that both mean the same thing though so...

Well, if 0^0 = 1, then 0^0 + 0^0 = 1 + 1 = 2, but here's the thing. 0^x = 0, but x^0 = 1.

Oh, you edited your post while I was typing my reply. WOOPS!

Yeah...sorry about that.

Your OG post said 0/0 was infinity, but then while I was typing my reply, you edited it.

It's ok.

Yeah I meant to say that it wasn't infinity, it was undefined.

Yeah. Now what about what I said about 0^0? And you didn't say anything about how the 0th root of a number involves infinity.

As for 1/0, we already touched on the concept that 0/0 is equal to...nothing. 1/0 as well, 1/0 is pretty much equal to, well, 1 x 0/0. But hold up! 1 x 0 is...0! How did we get 1/0?

You see, it still makes no sense!

The 0th root? Hm...I haven't gotten to that level of Math in my school, but I will try my best to explain the 0th root.

So you know Cube Roots and Square Roots, right? Basically you divide a number into equal parts that, when those equal parts multiply together, equal, well, the original number. I think so anyways, I'm not that good at explaining because we haven't gone in-depth into this sort of stuff.

But for the 0th root, if you take a number, say 2, and you root it down to the 0th root, then...there's nothing to divide. But hold up! Let's not jump to conclusions so fast!

Let's multiply 2 to the 0th root with, well, the 0th power. This means we just eliminated the 0th root radical or whatever, right? No...in my previous post, I said that 0 to the power of 0 is...nothing, null.

Okay nevermind I'll let someone else explain :sweat_smile:

Huh. I always thought that because x^0 = 1, then the 0th root of 1 = x, but that's true for all x! For 0th roots of other numbers, that's UNDEFINED because there is no x that x^0 = y, y is not 2.

can you please stop spamming about that? cant you open google and do research on your own? stop asking every single thing here, go and learn stuff yourself.

i am still gonna answer, but this is last time, i hate teaching. all those numbers involve undefined values. undefined and infinites both dont make sense, they are tightly connected.

for example, 1/0.1 = 10, 1/0.001 = 1000, 1/0.00001 = 100000, 1/0.000000..... = undefined, it approaches infinity.

in 0^0 and 0th root of a number it is more complex, think of them as undefined too.

cya.

Technically, they resolve to NaN according to IEEE-754. However, some implementations use ∞ and NaN interchangeably.

this got really off-topic...
atp, can't we just let this thing close?

Maybe.

i mean all this topic does is put a (now) useless topic at the top of the list and spam people's notifications...
it doesn't even provide useful information anymore, just random nonsense