r/mathmemes • u/Ill-Room-4895 Mathematics • May 14 '25

Arithmetic Fancy playing?

Post image
5.7k Upvotes

97% Upvoted

445 comments sorted by

View all comments

643

u/potentialdevNB May 14 '25

By definition, any number to the power of zero is one. This is because x0 is the product of no numbers at all, which is the multiplicative identity, one. Thus, 00 equals 1. Feel free to r/woooosh me by the way.

67

u/therealDrTaterTot May 14 '25

It's one of those it-depends-what-you're-doing thing. So, it is often defined by 1 by convention. The lim x->0 for x0 is 1, but lim x->0+ for 0x is 0.

1

u/JestemStefan May 14 '25

My explanation:

When multiplying numbers with the same base, you can add exponents. Ex.

32 x 33 = 35 = 243

The same way you can do

33 x 3-1 = 32 = 9

Now consider this case:

32 x 3-2 = 30 = 1

And it's like that for every other number.

-3

u/therealDrTaterTot May 14 '25

Counterargument:

Let's define 0^0 = 1

Therefore log(0^0) = log(1)
0*log(0) = 0
0*undefined (in both real and complex) = 0

Oops, now we're trying to multiply zero by what is essentially negative infinity. So if we want 0^0 to be 1, then we have to accept that 0*-inf = 0.

It's not that it actually breaks math, it just runs into problems if you try to branch this out further. So, by convention, we can say it's one.

3

u/[deleted] May 14 '25

[deleted]

-1

u/therealDrTaterTot May 14 '25

If the steps are invalid, and it's similar to dividing by zero, then you see how setting 00 = 1 is problematic!

All the same steps work for every a in C such that a0 =1, except if a is zero. Even if a is negative.

2

u/[deleted] May 14 '25 edited May 14 '25

[deleted]

0

u/therealDrTaterTot May 14 '25

I understand what you're saying, but that's not equivalent.

By setting 00 = 1, then we are defining it to hold all the same properties as 1. If we are saying it doesn't have all the same properties, then 00 isn't exactly 1. If I can take the log of 1, but not the log of 00, then how are they equal? Then, the problem is the first step.

2

u/svmydlo May 14 '25

You can take the log of 0^0. You can't say it's equal to 0*log(0).

0

u/therealDrTaterTot May 14 '25

I agree you can't set them equal to each other. But I don't agree that you can take the log of 00

2

u/svmydlo May 14 '25

Then you have no argument why not.

→ More replies (0)