Since I encourage students to always question the (rather confident) stuff that comes out of my mouth, they did.
So I proceeded to explain it… And got hung up!
0/0 is not undefined!
Turns out I was wrong. Infinitely wrong.
Let’s say 0/0 is 85. (Just join me on this journey – don’t freak yet.)
So 0/0 = 85, which means 85 x 0 = 0 and 0/85 = 0.
Which is just fine!
But the guy down the road might want 0/0 to be -72π instead. And it’d be just fine, too.
But then 0/0 = 85 and 0/0 = -72π.
And then you come along and want 0/0 to be 1,000,000.
Which means if I have $85, I also owe someone $72π, and I also have $1,000,000.
I assure you, I don’t have $1,000,000.
So 0/0 is indeterminate.
0/0 doesn’t not exist. It just exists as too many things. And when that happens, I’m a millionaire. And so are you.
In reality, this isn’t true.
At least about me.
Did you ever get this one confused? Share your thoughts in the comments!
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