If you cut a hole in a flat plane that extends infinitely in 4 directions is it still infinite?

Answer 1

No. (i guess)

consider a line - defined something like : extends indefinitely in both directions.

now consider to take away a section from it. It gets converted to 2 rays.

so logically a plane is also destroyed even if...

Answer 2

Infinite physical extension is actually impossible, so the question (though interesting) is also nonsensical. Something can be mathematically infinite in the sense that it is open-ended like pi, or the list of prime numbers. A physical form can be boundless, like a sphere, but it is still finite.

Answer 3

your question does not make sense, a plane is an imaginary concept and not a sheet of paper on which you can cut a hole, its like asking can i cut a hole in space! even if you do cut a hole in a plane you do not affect its reach for e.g you have a hand kerchief which is 20 inches by 20 inches, now if u cut a hole in it -it is still 20inch by 20 inch.

Answer 4

If you start counting at 2 are there still an infinite number of numbers?

But then again, would it still be a plane?

"Rabbi Krustofski, why do you always answer a question with a question?"

Rabbi Krustofski: "There's another way?"

Answer 5

Yes, because infinite minus any number is still infinite.

Answer 6

yeah you cant stop a plane thats infinite, its still be a hole and the plane would always be infinatly bigger than the hole.

Answer 7

I believe that it would not be infinite because there is a mising part. But I am not a mathematiian.

Answer 8

No.

This answer of course supposes you are using intergalactic pizza theory, invented by Earth Italians.

Eventually, you would hit a piece of pepperoni-- and we all know: flat or not, pepperoni is not to be argued with!

Happy researching!

Answer 9

Yes.

Answer 10

yes