There’s an advantage to understanding the non-arbitrary meaning of these signs - and that is: they are not the only inequality signs in existence.
If you need to remember crocodiles and pointy things, you’re going to have trouble remembering/understanding things like:
≫ (much greater than, sometimes written as >>)
≥ (greater than or equal to - commonly also written as >= )
≈ (approximately equal to)
≠ (not equal to)
The alligator thing doesn’t make any sense either. Animals tend to eat things that are smaller than themselves.
No. I’ve been using the alligator method since I was a child and I get all these, too, and don’t have problems with them. And I use about 20 more symbols every day - I’m taking discrete math, so we are doing congruence, and factorials, etc., etc.
I like the alligator analogy. It is simple and sticks in my head. I don’t understand why there is such a debate. If that’s what helps someone, that’s what helps someone. No one really knows how other people think, so why is one way the right way?
As to your signs, once you get equals and greater than/less than correct, the others just fall in line.
I would say the right side. And I would be right. And that’s yet another way of visualizing the symbol. You can show your kids a volume slider and have them imagine that.
I don’t know why you’re arguing this with me. It’s obvious that some people have problems knowing which side should be “less” and which side should be “more” from the existence of this thread. Ergo, not everyone finds it as blindingly obvious as you or me. You can point at them and laugh and imply they’re idiots for not knowing, or you can try to find a way to teach them. “Little-to-big”, “alligators,” or “Pac Man” whatever sticks.
Nope, never much bothered me, even though I visualize the Pac Man. (Plus you have to be aware that >> also means “shift right” in some contexts, so in that case the “>” really is an arrow pointing to the right meaning “move the bit over.” In fact, that’s the only context I ever run into “>>” and “<<”.) How is visualizing Pac Man any different than visualizing “small-to-big”? They’ve both visualizations.
I agree with pulykamell and others - the “direction” of the “arrow” is arbitrary. It may seem self-evident because the meaning is so ingrained (I can’t remember a time when I didn’t know what it meant) but there’s no logical reason why the symbol couldn’t “point” to the larger value.
If you’ve ever seen one of those diagrams in which a small section is expanded out into a separate box, to show more detail (I can’t find a good example of what I mean because it’s not easy to search for), the graphic that represents the expansion often resembles an inequality sign. But in this case, the thing on the “wide” end of the triangle is a subsection of the larger thing at the pointy end. So I don’t think we can say that it’s self-evident that the larger thing should go on the “wide” end of such symbols.
I’ve also never come across the “wonky equals sign” interpretation. The Wikipedia article doesn’t seem to support that idea.
The direction of the symbol is self-evident. It only seems arbitrary because so many people are taught to think of it as an arrow that points. The logical reason why the symbol doesn’t point to the larger value is that it doesn’t point at all.
But that in and of itself is arbitrary. Why does “lines farther apart” to “lines closer together” necessarily mean “bigger” to “smaller”? Nobody, as far as I know, is actually taught to think “>” and “<” are an arrow that points. Saying “>” is bigger to smaller is just as arbitrary to me as saying “>” points to the larger value (which it does not.) Both require context and learning. Who is to say that interpreting the “>” as an arrow is not a more instinctual interpretation of the sign?
I guess because it obscures the simpler, non-arbitrary meaning of the symbols, and because it comes across as silly/juvenile, in a field not commonly associated with silliness.
blink blink
How horrible indeed for a grade school analogy to seem silly and juvenile. Similarly, My Very Earnest Mother Just Sent Us Noodles is an affront to the noble field of cosmology.
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Which side of that symbol is bigger, the left side or the right side?
The wikipedia article doesn’t provide any reasoning for the choice of the symbol, so it doesn’t rule it out either.
What’s curious, and may yet unravel the ‘non-arbitrary meaning’ arguments I and others have made in this thread, is that the reason the equals sign (=) was chosen was that the ***length ***of the two lines is equal, not their spacing.
But on some level, it is arbitrary. It may be based on a logically defensible premise, but I can easily see the reverse of the symbols being logically defensible and the same sort of argument ensuing here.
At any rate, these types of visualizations I find helpful (and I feel “small-to-large” is a visualization, too, that takes up as much processing time as thinking of the symbol as a mouth eating the bigger number.) With enough use, eventually they should fall into natural use and you might not need them except as a double-check on your memory. I don’t see anything wrong with reinforcing knowledge in this way.
Good point, I guess, but mnemonics don’t seem to me the same category of thing as stories about crocodiles (YMMV)
Neither are “bigger” to me. The right side has lines farther apart. The left has lines closer together. Why this necessarily and self-evidently must mean “lesser” and “greater” is beyond me.
It’s not a whole story. I mean, it may be initially presented as one to get the kids involved and listening. It’s just a way to visualize what’s going on. I’m not even sure the Pac Man I use was taught–I think it’s just something I came up with because that was the easiest for me to remember. It’s not like I run through an entire narrative to decide whether “>” means “greater” or “<” means “lesser.” For me, it’s quicker to think of “>” as chomping the bigger number than to visualize the “>” as bigger-getting-smaller.
The crocodile eats the bigger number is a mnemonic.
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Take a ruler, and measure the marks present on the left side of the symbol, the point. Then measure the marks present on the right side of the symbol, two points separated by a distance.
Are the measurements different? If they are, then one of the sides is unambiguously and non-arbitrarily bigger than the other.
“Arbitrary” is an alligator eating the bigger number. Why doesn’t the alligator eat the smaller number? Arbitrary is King Kong pointing at the small person. Why not a leprechaun pointing at the big person? Arbitrary is < looking “like” an L for Lesser Than, why not looking like an L for Larger Than?
They’re non- arbitrarily farther from each other. But that doesn’t automatically mean to me that it should mean “bigger.” You disagree. Fine. Without context, if I was presented with “A < B” having absolutely no previous knowledge of inequality symbols, I would not bet either way, as I find both interpretations equally logical and defensible.
This sounds like all arguments where one side is just accustomed to something (a sport, a symbol, a unit of measurement) and then tries to make the argument that their understanding of it reveals how perfect and simple it is.
It’s a symbol, not a natural law. A different symbol could have been chosen, and not all symbols are in any way representational. We could flip the meanings of < and > and in no way violate any laws of nature.