What is the difference between “I have little money” and “I have a little money”?
Are they the same?
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There is a difference in meaning between “a little” and “little”.
The meaning of “a little” is positive. It means some or a small amount, such as, “I have a little money.”, “He made a little progress.”, etc.
On the other hand, “little” has a negative meaning. It means an extremely small amount or an amount that is less than expected or wished for, as in, “I have little money.”, “He made little progress.”, etc.
If we look at these sentences, the difference between “a little” and “little” will come across easily. The former may be satisfactory for a particular purpose while the latter is not.
"I have little money" implies you have a very small amount of money, and usually less than you'd want to. For example, when your kid asks you to buy him a toy, and you reply "Sorry, I have little money", it implies you can't afford the toy.
"I have a little money" implies that while the sum in question might not be big (relatively speaking), it's good enough. When you tell your kid "Well, I have a little money", you're affirming that you can, in fact, afford the toy.
I have little money = I am not a rich man.
I have a little money can mean:
a. I have some money on my person now (e.g. in my pocket) but not very much.
b. I have a rather large sum of money available if I should need it (i.e. litotes/understatement)
"little money" means not much as in "I can't afford to buy a new dress. I have little money."
"a little money" can be positive as in "What about going to the cinema? I would invite you. I have a little money I can spend."
Using the article a/an has a subtle effect on the meaning of the sentence.
Below are my thoughts on your question.
The other answers are all correct, but they omit one detail that might clarify the usage: "a little" is a shortened version of the full phrase "a little bit of."
Therefore, the phrase "I have a little money" is in fact an abbreviation of "I have a little bit of money." Hopefully this will make it more clear as to why it is a positive amount: it means you may not have much, but you do in fact have some. You have a bit (syn. portion or amount) of money, you just have "a little bit."
a little = some
little = not much