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Infinity minus infinity is…. zero?

Hey Guys! So a couple days ago, a friend of ours, my roommate and I were sitting in our room and somehow the concept of inifity came up. Being students of science, we had to explore an idea. My roommate doesn’t really believe in the concept of different sizes of inifinity, at least from an application in the real world stand point, which makes sense since he thinks about things more practically than theoretically.

So the point of the discussion was focussed on one key question… if my roommate gave our friend infinite toothpaste and then he took away infinite toothpaste from my friend shortly after, does he necessarily now have no toothpaste at all? From the perspective of my friend (who will now be named "Juan" since I don’t want to keep typing "my friend") and I, that situation doesn’t imply zero toothpaste since we were thinking about the relative sizes of infinity. If he gave Juan infinite toothpaste at the size of the real numbers and then took away infinite toothpaste at the size of the natural numbers then Juan would still have infinite toothpaste.
My roommate’s argument was that from a practical standpoint if I give someone an infinite amount of something and then take away an infinite amount, then they’re left with zero.

Which do you agree with?

Also, this weekend was the annual Indian Students Association’s (OASIS) show which included various performances and a fashion show featuring yours truly. Muneeb was co-MC with a grad student named Parul. Here are some pictures!

Alright that’s all for now.

See you guys soon,

Brad Chattergoon