Can Infinite X Infinite Be Greater Than Infinity?

2026-04-17 09:43:31 189
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3 Answers

Flynn
Flynn
2026-04-20 23:54:03
From a physics student's perspective, infinity feels more like a placeholder for 'we don't have the tools to measure this yet.' When cosmologists talk about the universe being infinite, they mean it's unbounded—not that it literally contains infinite stars or galaxies in a way we could quantify. So if someone asks if infinite × infinite is greater, I'd say it depends on the framework. In practical terms? Probably not. But mathematically, sure, because infinity isn't a number; it's a concept we manipulate with rules. Like Hilbert's paradox of the Grand Hotel: you can always 'make space' for more guests even if it's 'full,' which hints at how slippery these operations are.

I once tried visualizing this by imagining two endless grids—one for time, one for space. Even if both are infinite, combining them doesn't automatically create something 'bigger.' It just extends dimensions. That's where analogies fail, though, because human brains aren't wired to grasp actual infinities. We approximate.
Zander
Zander
2026-04-22 20:06:51
The concept of infinity has always fascinated me, especially when you start playing around with different 'sizes' of it. In math, not all infinities are created equal. Take the natural numbers (1, 2, 3...) versus the real numbers (all points on a number line). The latter is uncountably infinite, while the former is countably infinite. When you multiply two countably infinite sets (like natural numbers × natural numbers), you still end up with a countably infinite set—it doesn't 'grow' bigger. But when dealing with higher cardinalities, like the power set of an infinite set, things explode into larger infinities. It's wild how our intuition breaks down here—infinity isn't just a static 'endless' thing but has layers almost like an onion.

What really messed with my head was learning about Cantor's diagonal argument, proving that some infinities are fundamentally larger than others. The idea that you can't even list all real numbers in any order, no matter how clever, while you can with natural numbers? That distinction makes 'infinite × infinite' questions hinge entirely on what kind of infinity you're dealing with. For me, this stuff is less about cold math and more like poetry—there's beauty in how these abstract concepts stretch our minds beyond everyday logic.
Nathan
Nathan
2026-04-23 21:20:15
Honestly, my gut reaction to this was 'infinity is already endless—how can multiplying it change that?' But after binging some pop-math videos, I learned that mathematicians treat infinities like different breeds of dragons. Some are fire-breathing and uncountable (like the real numbers), while others are more like orderly, countable serpents (like integers). The product of two countable infinities stays tame, but toss uncountable ones into the mix, and suddenly you're dealing with a beast that makes Cantor lose sleep. It's less about 'greater than' and more about 'different flavors of endless.' Still blows my mind that infinity comes with a hierarchy.
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