The Gemara in Bava Kamma 119a teaches that one who robs another of even a perutah's worth is considered as though he has taken his life, deriving this from the verses describing how greed for unjust gain destroys the owner's sustenance and even his children, and Mesillat Yesharim 11 cites this teaching to underscore the gravity of theft even in a minuscule amount.
The codifiers establish that the Torah prohibition of theft attaches even below the monetary threshold of a perutah: Mishneh Torah, Robbery and Lost Property 1:1 rules that stealing anything worth a perutah violates the lo taaseh of lo tignov, while Sefer HaChinukh 229:1 clarifies that although the formal prohibition of gezeilah only technically applies at a perutah's value, taking less than that remains forbidden mi'd'oraita as a chatzi shiur, a position echoed by Arukh HaShulchan, Choshen Mishpat 348 and by Sdei Chemed, Maarechet Gimel 36, who likewise treats sub-perutah theft as biblically forbidden under the chatzi shiur principle.
The Shulchan Arukh codifies that one may not steal anything at all, even as a joke, even with intent to return it, pay double, or merely to upset the owner, precisely so that a person not become habituated to theft, as stated in Shulchan Arukh, Choshen Mishpat 348, a ruling that traces back to the Sifra's drashah on lo tignovu in Sifra, Kedoshim, Section 2:2 and is likewise recorded by Sefer HaChinukh 224 and Sefer HaMitzvot, Negative Commandments 244 and Sefer Mitzvot Gadol, Negative Commandments 155.
The Gemara in Sanhedrin 57a shows that even an amount a Jew would ordinarily forgive still causes distress at the moment of taking and is therefore punishable, while Eruvin 62a rules that for a gentile, who does not waive rights over small amounts, the prohibition against theft applies to any value whatsoever since nothing is deemed too small to count as his property.
Modern poskim extend this principle practically: Rav Eliezer Melamed (Peninei Halakhah, Likkutim II 4:3) rules that taking any object of another without permission is forbidden even if its value is negligible, down to a small spoon or a match, though he carves out an exception for inconsequential items that people customarily do not mind lending implicitly, and in Rav Eliezer Melamed (Peninei Halakhah, Likkutim II 4:14) he applies this to workplace settings, such as using a telephone or making calls beyond what an employer has authorized.
Rav Ovadia Yosef (Maayan Omer 10:6:23) addresses the halachic status of taking property worth less than a perutah, holding that it is treated as a chatzi shiur of the Torah's monetary prohibition and is forbidden min haTorah even against a fellow Jew.
Rav Menashe Klein (Mishneh Halachos 9:376) takes up the question of whether repeated sub-perutah thefts combine into a culpable amount, reasoning that while an isolated small theft is generally assumed to be forgiven by the owner, a pattern of repeated takings reveals that the owner never truly intended forgiveness, so the amounts may be aggregated.
Further applications surface throughout the modern responsa literature: Rav Ovadia Yosef (Maayan Omer 10:6:5) reiterates that stealing is forbidden by Torah law in any amount and even as a joke or with intent to return it, while Avnei Yashfeh 3:116 confirms that taking even a small amount is genuine theft, and Avnei Yashfeh 6:150 and Avnei Yashfeh 7:128 apply this principle respectively to borrowing without permission with intent to repay and to falsely claiming compliance for insurance purposes.
The theme of deception as a form of theft of the mind also appears in the sources: Chullin 94a records Shmuel's teaching that it is forbidden to deceive people, even a gentile, and Sefer Mitzvot Gadol, Negative Commandments 155 likewise cites this principle alongside the prohibition on stealing any amount.