The person who wrote that was wrong. > does not mean less than.
Right. The lack of “is” is what makes it ungrammatical. The OP, and general English phrasing, includes the verb: “All my apples are >1lb”. I would say that “All my apples >1lb”, with an implicit “are”, is wrong. I’ve certainly never seen that usage.
And yes, the reversed phrasing isn’t ungrammatical, but I would say it is nonsensical. There are certain idiomatic ways of talking about sets, and this isn’t one of them. “1 lb is less than the weight of each of my apples” would be fine (just a little wordy), and closer to the mathematical equivalent (which would require a “for each” to pick out an element of the set).
I mean, the takeaway here is, if you’re going to use these symbols in a sentence that isn’t really about maths, you’d better at least use the correct symbol for the general meaning. Once you use the wrong one, people will no longer just pass over it, then it all unravels.
Agreed; my point is just that “>” is literally just the words “greater than” when used in a sentence, in the same way that “&” is “and”. So if there’s any confusion about the meaning, just do the substitution and the interpretation should be obvious.
Thank you all! I knew you’d come through!
Some of the forums I frequent are filled with you younger people and I tend to oversimplify my posts there and forget to be more concise and precise when I post at other more mature oriented forums like this!
I had the same problem when I ran a store with a bunch of 20 somethings!
I would contend that it is in fact what those symbols mean. It sometimes happens, on a crowded whiteboard, that two quantities one wishes to compare are arranged vertically with respect to each other, not horizontally. And when that happens, one might draw an angle bracket on the board, aligned vertically, with the point towards the smaller quantity, and the open end towards the larger quantity. Something like, instead of 3 < 5 or 5 > 3,
3
^
5
I would contend that all three of these usages use the same symbol, and that all three are equally understandable to anyone who understands the use of that symbol.
And what I remember, though I don’t know if I was taught that or came up with it on my own, is that < angled a little differently looks like L – L for “less”.
I certainly wasn’t taught anything about alligators. Unless we count ‘see you later, alligator!’, which has nothing to do with “less than” signs.
A comparison being abbreviated with ‘<’ assumes a lot of information from context. ‘All my apples are greater than 1 lb.’ is no more clear than ‘All my apples > 1 lb.’. Look at how much information is missing that must be derived from context, not from a simple substitution, ‘The weight in lbs. of all my apples is greater than 1 lb.’. ‘Greater than’ and ‘>’ both refer to a numeric comparison in this usage, and both sides of the operator need to be expressed with a number and units.
I think it’s a bit overly pedantic to quibble over whether a sentence with < or > is grammatical or not depending on whether the word “is” or “are” is also present. I’ve always understood that > could be read as “greater than” or “is greater than” as needed, and likewise <
The equal sign = could be read as “equals” or “is equal to” or even, more explicitly, as “is the same number as”.
In all cases, I view the symbols < = and > as “state-of-being verbs” or, if pronounced as “is the same number as”, it’s still a state-of-being verb phrase.
I have it on good authority (to-wit my 7th grade science teacher) that in Texas, many mosquitoes weigh > 1 lb.
Concur. If someone says “All my apples are greater than 1lb.”, what goes through my mind is:
Those are some pretty big apples if they are all heavier than a pound… wait… that can’t be right… maybe they mean the total weight of apples is greater than a pound… but wait… that’s hardly a remarkable statement… so this example statement is not a great one.
In casual usage though, > can just be assumed to mean ‘(is) bigger than’ or ‘(is) superior to’ - in fact, I see this a lot in online commentary in statements of the form ‘My dog > your cat’ - which doesn’t make any sense to try to interpret as a strict mathematical statement, since there is only one dog and one cat.
True, but that’s true of pretty much any non-mathematical statement. Hence my claim that it is an abbreviation, not a mathematical symbol. The less ambiguous statement would be something like ∀x∈MyApples Weight(x) < 1 lb. Natural language sometimes has ambiguities that can only be resolved with additional context.
(Just for context, I’m in my sixties.) This is the first time I’ve heard of this “alligator” mnemonic. To me, it was always intuitive that the larger value is on the wide side of the arrow, and the smaller value is on the pointy side. (But I confess that I learned this so long ago that I have no idea whether that was from a teacher or I intuited it myself.)
In any case, I’d like to point out that a very similar convention appears in much software. Imagine you are looking at some sort of grid on your screen, displayed as rows and columns. An address list is a great example, where each person is on another line, and you have columns for name, street, city, and zip code. Suppose further that by clicking on a column heading, you will sort the table by that column, and clicking a second time will sort it in reverse order.
In such cases, you’ll very often find a small triangle at the top of the column. “
” means “top is less than bottom”, so that the column is sorted 0-9 or A-Z. “
” means “top is greater than bottom”, so that the column is sorted 9-0 or Z-A. The convention is almost identical to < and >, except that it is vertical instead of horizontal, and a filled-in triangle instead of a V-shape.
I have long wanted to point this out to someone, but this thread is the first time I found anyone nerdy enough to care. 
The wider/narrower thing is actually the origin of the symbol, I believe, but from previous conversations about this on the board, there are people who have genuine problems perceiving one end of the symbol as ‘wide’ and the other end as ‘narrow’. I think this relates to the fact that the lines on one end of the symbol meet at a point; if it were like a sideways version of the ‘road narrows ahead’ sign (below) this would not be so hard:
Same age.
I agree the alligator thing wasn’t taught when / where I went through. But we were explicitly taught “the big end is the big number; the small end is the small number” as a way to remember which is which. Which somehow a lot of kids, myself included, found harder that you’d (I’d) expect at first glance.
That mnemonic nicely generalizes to vertical ordering examples as @Chronos said a few posts ago and as you say as well.
Based on some teachers in my extended family I think the difference is these concepts are introduced to younger kids nowadays than backe in Ye Olden Tymes and so the mnemonics used are more “kid-friendly” now than they were then.
Back in the old days, teachers were allowed to beat the knowledge in with sticks, if it didn’t go in naturally
Say what? Big things eat smaller things. (Usually 
x is less than y : x < y
S is a subset of T : S ⊆ T
H is a subgroup of G : H ≤ G
Or H is less than or equal to G. Depends on how you pronounce ‘≤’.
If you’re hungry, would you rather have a big hamburger or a tiny hamburger? That’s what the alligator is choosing between. I think.
In places like Facebook, which has no bold or italic buttons, I’ve seen some people use them to emphasize a . I thought that’s what this topic was going to be about.
In the early 1970s when I was learning about > and <, I had difficulty with right and left, so teachers demanding that I know that the one that’s open to the left is “less than” and the one open to the right was “greater than” caused me difficulty. My current point of view is that the symbol relates two quantities, and it is open on the side that has the larger quantity. I’d read “1 < 3” as “3 is greater than 1” or “1 is less than 3”, depending on my mood.
“Apples > 1 pound” is somewhat ambiguous, but in context (next to a table full of large apples) it’s pretty clear it means “each of these apples weighs more than a pound” - in a different context (next to a basket of little apples) it would mean “This basket of apples weighs more than a pound”.