3 added link, reformatted and minor edits
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The Rambam in Hilchos Tzitzis 1:4 writes:

הַתְּכֵלֶת אֵינוֹ מְעַכֵּב אֶת הַלָּבָן וְהַלָּבָן אֵינוֹ מְעַכֵּב אֶת הַתְּכֵלֶת. כֵּיצַד. הֲרֵי שֶׁאֵין לוֹ תְּכֵלֶת עוֹשֶׂה לָבָן לְבַדּוֹ. וְכֵן אִם עָשָׂה לָבָן וּתְכֵלֶת וְנִפְסַק הַלָּבָן וְנִתְמַעֵט עַד הַכָּנָף וְנִשְׁאַר הַתְּכֵלֶת לְבַדּוֹ כָּשֵׁכָּשֵׁר‏

The absence of the blue thread does not bar the use of the white fringe. Nor does the absence of the white fringe prevent the use of the blue thread. How so? If a person has no blue thread, he puts in the white fringe alone. So too, if the white fringe and the blue thread have been attached and the white fringe has been severed and diminished up to the corner of the garment and only the blue thread was left, it is fit for use.

The Kesef Mishneh explains the logic and I gathered (though I didn't pour over it) that he traces it to the posuk for tzitzis which says that the ptil techeilet is added to what is already an extant "tzitzit." The techeilet becomes its own mitzvah. Hilchos Tzitzis 1:9 gives the method for tying plain white threads.

Interestingly, the Rambam closes out the second perek (2:9) by writing:

קשה עונש מי שאינו מניח לבן, יתר מעונש מי שלא הניח תכלת: לפי שהלבן, מצוי לכול; והתכלת, אינה מצויה לכול--לפי שאינה מצויה בכל מקום ולא בכל זמן, מפני הצבע שאמרנושאמרנו‏

Not to attach white fringes to one's garment is more culpable than to omit the blue thread. For the white fringes are procurable by all, while the blue thread cannot be obtained in all places and at all times on account of the need of the special dye, of which we have spoken.

This references the braisa on Menachos 43b quoting R' Meir which, it seems, shows that the gemara accepted the idea of plain white tzitzis.

The Rambam in Hilchos Tzitzis 1:4 writes:

הַתְּכֵלֶת אֵינוֹ מְעַכֵּב אֶת הַלָּבָן וְהַלָּבָן אֵינוֹ מְעַכֵּב אֶת הַתְּכֵלֶת. כֵּיצַד. הֲרֵי שֶׁאֵין לוֹ תְּכֵלֶת עוֹשֶׂה לָבָן לְבַדּוֹ. וְכֵן אִם עָשָׂה לָבָן וּתְכֵלֶת וְנִפְסַק הַלָּבָן וְנִתְמַעֵט עַד הַכָּנָף וְנִשְׁאַר הַתְּכֵלֶת לְבַדּוֹ כָּשֵׁ

The absence of the blue thread does not bar the use of the white fringe. Nor does the absence of the white fringe prevent the use of the blue thread. How so? If a person has no blue thread, he puts in the white fringe alone. So too, if the white fringe and the blue thread have been attached and the white fringe has been severed and diminished up to the corner of the garment and only the blue thread was left, it is fit for use.

The Kesef Mishneh explains the logic and I gathered (though I didn't pour over it) that he traces it to the posuk for tzitzis which says that the ptil techeilet is added to what is already an extant "tzitzit." The techeilet becomes its own mitzvah. Hilchos Tzitzis 1:9 gives the method for tying plain white threads.

Interestingly, the Rambam closes out the second perek (2:9) by writing:

קשה עונש מי שאינו מניח לבן, יתר מעונש מי שלא הניח תכלת: לפי שהלבן, מצוי לכול; והתכלת, אינה מצויה לכול--לפי שאינה מצויה בכל מקום ולא בכל זמן, מפני הצבע שאמרנו

Not to attach white fringes to one's garment is more culpable than to omit the blue thread. For the white fringes are procurable by all, while the blue thread cannot be obtained in all places and at all times on account of the need of the special dye, of which we have spoken.

This references the braisa on Menachos 43b quoting R' Meir which, it seems, shows that the gemara accepted the idea of plain white tzitzis.

The Rambam in Hilchos Tzitzis 1:4 writes:

הַתְּכֵלֶת אֵינוֹ מְעַכֵּב אֶת הַלָּבָן וְהַלָּבָן אֵינוֹ מְעַכֵּב אֶת הַתְּכֵלֶת. כֵּיצַד. הֲרֵי שֶׁאֵין לוֹ תְּכֵלֶת עוֹשֶׂה לָבָן לְבַדּוֹ. וְכֵן אִם עָשָׂה לָבָן וּתְכֵלֶת וְנִפְסַק הַלָּבָן וְנִתְמַעֵט עַד הַכָּנָף וְנִשְׁאַר הַתְּכֵלֶת לְבַדּוֹ כָּשֵׁר‏

The absence of the blue thread does not bar the use of the white fringe. Nor does the absence of the white fringe prevent the use of the blue thread. How so? If a person has no blue thread, he puts in the white fringe alone. So too, if the white fringe and the blue thread have been attached and the white fringe has been severed and diminished up to the corner of the garment and only the blue thread was left, it is fit for use.

The Kesef Mishneh explains the logic and I gathered (though I didn't pour over it) that he traces it to the posuk for tzitzis which says that the ptil techeilet is added to what is already an extant "tzitzit." The techeilet becomes its own mitzvah. Hilchos Tzitzis 1:9 gives the method for tying plain white threads.

Interestingly, the Rambam closes out the second perek (2:9) by writing:

קשה עונש מי שאינו מניח לבן, יתר מעונש מי שלא הניח תכלת: לפי שהלבן, מצוי לכול; והתכלת, אינה מצויה לכול--לפי שאינה מצויה בכל מקום ולא בכל זמן, מפני הצבע שאמרנו‏

Not to attach white fringes to one's garment is more culpable than to omit the blue thread. For the white fringes are procurable by all, while the blue thread cannot be obtained in all places and at all times on account of the need of the special dye, of which we have spoken.

This references the braisa on Menachos 43b quoting R' Meir which, it seems, shows that the gemara accepted the idea of plain white tzitzis.

2 added link, reformatted and minor edits
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The Rambam, in Hilchos Tzitzis (halacha 4) reads ד התכלת, אינו מעכב את הלבן; והלבן, אינו מעכב את התכלת. כיצדHilchos Tzitzis 1:4 writes: הרי שאין לו תכלת, עושה לבן לבדו; וכן אם עשה לבן ותכלת, ונפסק הלבן, ונתמעט עד הכנף, ונשאר התכלת לבדו--כשר.

The [absence of] techelet does not prevent [the mitzvah from being fulfilled with] the white strands, nor does the [absence of] the white strands prevent [the mitzvah from being fulfilled with] techelet.

What is implied? A person who does not have techelet should make [tzitzit] from white strands alone. Similarly, if [tzitzit] were made from both white strands and techelet, and afterwards, the white strands snapped and were reduced until [they did not extend beyond] the corner [of the garment], and thus only the techelet remained, it is acceptable.

(text from http://mechon-mamre.org/i/2401.htm translation from http://www.tallit-shop.com/halacha-of-tzitzit-rambam/)

הַתְּכֵלֶת אֵינוֹ מְעַכֵּב אֶת הַלָּבָן וְהַלָּבָן אֵינוֹ מְעַכֵּב אֶת הַתְּכֵלֶת. כֵּיצַד. הֲרֵי שֶׁאֵין לוֹ תְּכֵלֶת עוֹשֶׂה לָבָן לְבַדּוֹ. וְכֵן אִם עָשָׂה לָבָן וּתְכֵלֶת וְנִפְסַק הַלָּבָן וְנִתְמַעֵט עַד הַכָּנָף וְנִשְׁאַר הַתְּכֵלֶת לְבַדּוֹ כָּשֵׁ

The absence of the blue thread does not bar the use of the white fringe. Nor does the absence of the white fringe prevent the use of the blue thread. How so? If a person has no blue thread, he puts in the white fringe alone. So too, if the white fringe and the blue thread have been attached and the white fringe has been severed and diminished up to the corner of the garment and only the blue thread was left, it is fit for use.

The kesef MishnehKesef Mishneh explains the logic and I gathered (though I didn't porepour over it) that he traces it to the posuk for tzitzis which says that the ptil techeilet is added to what is already an extant "tzitzit" (left column, the pasuk is on the third line http://hebrewbooks.org/pdfpager.aspx?req=9713&st=&pgnum=229&hilite= )"tzitzit. The" The techeilet becomes its own mitzvah. Halacha 9 in perek 1Hilchos Tzitzis 1:9 gives the method for tying plain white threads.

Interestingly, the rambamRambam closes out the second perek 2 with קשה עונש מי שאינו מניח לבן, יתר מעונש מי שלא הניח תכלת(2:9) by writing: לפי שהלבן, מצוי לכול; והתכלת, אינה מצויה לכול--לפי שאינה מצויה בכל מקום ולא בכל זמן, מפני הצבע שאמרנו

The punishment given someone who does not wear [tzitzit of white strands] is more severe than that given one who does not wear techelet, because the white strands are easily accessible while techelet is not available in every time and in every era, because of the [unique] dye mentioned above.

קשה עונש מי שאינו מניח לבן, יתר מעונש מי שלא הניח תכלת: לפי שהלבן, מצוי לכול; והתכלת, אינה מצויה לכול--לפי שאינה מצויה בכל מקום ולא בכל זמן, מפני הצבע שאמרנו

Not to attach white fringes to one's garment is more culpable than to omit the blue thread. For the white fringes are procurable by all, while the blue thread cannot be obtained in all places and at all times on account of the need of the special dye, of which we have spoken.

thisThis references the braisabraisa on menachos 43bMenachos 43b quoting r.R' Meir which, it seems, shows that the gemara accepted the idea of plain white tzitzis.

The Rambam, in Hilchos Tzitzis (halacha 4) reads ד התכלת, אינו מעכב את הלבן; והלבן, אינו מעכב את התכלת. כיצד: הרי שאין לו תכלת, עושה לבן לבדו; וכן אם עשה לבן ותכלת, ונפסק הלבן, ונתמעט עד הכנף, ונשאר התכלת לבדו--כשר.

The [absence of] techelet does not prevent [the mitzvah from being fulfilled with] the white strands, nor does the [absence of] the white strands prevent [the mitzvah from being fulfilled with] techelet.

What is implied? A person who does not have techelet should make [tzitzit] from white strands alone. Similarly, if [tzitzit] were made from both white strands and techelet, and afterwards, the white strands snapped and were reduced until [they did not extend beyond] the corner [of the garment], and thus only the techelet remained, it is acceptable.

(text from http://mechon-mamre.org/i/2401.htm translation from http://www.tallit-shop.com/halacha-of-tzitzit-rambam/)

The kesef Mishneh explains the logic and I gathered (though I didn't pore over it) that he traces it to the posuk for tzitzis which says that the ptil techeilet is added to what is already an extant "tzitzit" (left column, the pasuk is on the third line http://hebrewbooks.org/pdfpager.aspx?req=9713&st=&pgnum=229&hilite= ). The techeilet becomes its own mitzvah. Halacha 9 in perek 1 gives the method for tying plain white threads.

Interestingly, the rambam closes out perek 2 with קשה עונש מי שאינו מניח לבן, יתר מעונש מי שלא הניח תכלת: לפי שהלבן, מצוי לכול; והתכלת, אינה מצויה לכול--לפי שאינה מצויה בכל מקום ולא בכל זמן, מפני הצבע שאמרנו

The punishment given someone who does not wear [tzitzit of white strands] is more severe than that given one who does not wear techelet, because the white strands are easily accessible while techelet is not available in every time and in every era, because of the [unique] dye mentioned above.

this references the braisa on menachos 43b quoting r. Meir which, it seems, shows that the gemara accepted the idea of plain white tzitzis.

The Rambam in Hilchos Tzitzis 1:4 writes:

הַתְּכֵלֶת אֵינוֹ מְעַכֵּב אֶת הַלָּבָן וְהַלָּבָן אֵינוֹ מְעַכֵּב אֶת הַתְּכֵלֶת. כֵּיצַד. הֲרֵי שֶׁאֵין לוֹ תְּכֵלֶת עוֹשֶׂה לָבָן לְבַדּוֹ. וְכֵן אִם עָשָׂה לָבָן וּתְכֵלֶת וְנִפְסַק הַלָּבָן וְנִתְמַעֵט עַד הַכָּנָף וְנִשְׁאַר הַתְּכֵלֶת לְבַדּוֹ כָּשֵׁ

The absence of the blue thread does not bar the use of the white fringe. Nor does the absence of the white fringe prevent the use of the blue thread. How so? If a person has no blue thread, he puts in the white fringe alone. So too, if the white fringe and the blue thread have been attached and the white fringe has been severed and diminished up to the corner of the garment and only the blue thread was left, it is fit for use.

The Kesef Mishneh explains the logic and I gathered (though I didn't pour over it) that he traces it to the posuk for tzitzis which says that the ptil techeilet is added to what is already an extant "tzitzit." The techeilet becomes its own mitzvah. Hilchos Tzitzis 1:9 gives the method for tying plain white threads.

Interestingly, the Rambam closes out the second perek (2:9) by writing:

קשה עונש מי שאינו מניח לבן, יתר מעונש מי שלא הניח תכלת: לפי שהלבן, מצוי לכול; והתכלת, אינה מצויה לכול--לפי שאינה מצויה בכל מקום ולא בכל זמן, מפני הצבע שאמרנו

Not to attach white fringes to one's garment is more culpable than to omit the blue thread. For the white fringes are procurable by all, while the blue thread cannot be obtained in all places and at all times on account of the need of the special dye, of which we have spoken.

This references the braisa on Menachos 43b quoting R' Meir which, it seems, shows that the gemara accepted the idea of plain white tzitzis.

1
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The Rambam, in Hilchos Tzitzis (halacha 4) reads ד התכלת, אינו מעכב את הלבן; והלבן, אינו מעכב את התכלת. כיצד: הרי שאין לו תכלת, עושה לבן לבדו; וכן אם עשה לבן ותכלת, ונפסק הלבן, ונתמעט עד הכנף, ונשאר התכלת לבדו--כשר.

The [absence of] techelet does not prevent [the mitzvah from being fulfilled with] the white strands, nor does the [absence of] the white strands prevent [the mitzvah from being fulfilled with] techelet.

What is implied? A person who does not have techelet should make [tzitzit] from white strands alone. Similarly, if [tzitzit] were made from both white strands and techelet, and afterwards, the white strands snapped and were reduced until [they did not extend beyond] the corner [of the garment], and thus only the techelet remained, it is acceptable.

(text from http://mechon-mamre.org/i/2401.htm translation from http://www.tallit-shop.com/halacha-of-tzitzit-rambam/)

The kesef Mishneh explains the logic and I gathered (though I didn't pore over it) that he traces it to the posuk for tzitzis which says that the ptil techeilet is added to what is already an extant "tzitzit" (left column, the pasuk is on the third line http://hebrewbooks.org/pdfpager.aspx?req=9713&st=&pgnum=229&hilite= ). The techeilet becomes its own mitzvah. Halacha 9 in perek 1 gives the method for tying plain white threads.

Interestingly, the rambam closes out perek 2 with קשה עונש מי שאינו מניח לבן, יתר מעונש מי שלא הניח תכלת: לפי שהלבן, מצוי לכול; והתכלת, אינה מצויה לכול--לפי שאינה מצויה בכל מקום ולא בכל זמן, מפני הצבע שאמרנו

The punishment given someone who does not wear [tzitzit of white strands] is more severe than that given one who does not wear techelet, because the white strands are easily accessible while techelet is not available in every time and in every era, because of the [unique] dye mentioned above.

this references the braisa on menachos 43b quoting r. Meir which, it seems, shows that the gemara accepted the idea of plain white tzitzis.